Question 1

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. What is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = 48 ÷ 3 = 16 km/h. Step 2: Upstream speed = 48 ÷ 6 = 8 km/h. Step 3: Speed of boat in still water = (Downstream speed + Upstream speed) ÷ 2 = (16 + 8) ÷ 2 = 12 km/h. Therefore, the answer is 12 km/h.

Question 2

A boat travels 36 km downstream in 2 hours and the speed of the stream is 3 km/h. What is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = Distance / Time = 36 / 2 = 18 km/h. Step 2: Downstream speed = Boat speed + Stream speed → 18 = Boat speed + 3. Step 3: Boat speed = 18 - 3 = 15 km/h. Therefore, the answer is 15 km/h.

Question 3

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. What is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = 48 ÷ 3 = 16 km/h. Step 2: Upstream speed = 48 ÷ 6 = 8 km/h. Step 3: Speed of boat in still water = (Downstream speed + Upstream speed) ÷ 2 = (16 + 8) ÷ 2 = 12 km/h. Therefore, the answer is 12 km/h.

Question 4

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. A man swims at a constant speed in still water. What is the speed of the current?

Accepted Answer

Step 1: Downstream speed = 48 ÷ 3 = 16 km/h. Step 2: Upstream speed = 48 ÷ 6 = 8 km/h. Step 3: Speed of current = (Downstream speed − Upstream speed) ÷ 2 = (16 − 8) ÷ 2 = 4 km/h. Therefore, the answer is 4 km/h.

Question 5

A boat travels 48 km downstream in 3 hours and the same distance upstream in 4 hours. If the boat is to travel from point A to point B (84 km apart) downstream and then return to point A, what is the total time taken for the round trip?

Accepted Answer

Step 1: Find downstream speed. Downstream speed = 48/3 = 16 km/h. Step 2: Find upstream speed. Upstream speed = 48/4 = 12 km/h. Step 3: Time to travel 84 km downstream = 84/16 = 5.25 hours. Step 4: Time to travel 84 km upstream = 84/12 = 7 hours. Step 5: Total time = 5.25 + 7 = 12.25 hours = 12 hours 15 minutes. Converting to hours as decimal: 12.25 hours or 49/4 hours. As a mixed number or decimal answer option, this equals 12 hours 15 minutes or 12¼ hours.

Question 6

A boat travels 48 km downstream in 3 hours and 48 km upstream in 4 hours. A man swims at a constant speed in still water. If the man swims the same 48 km downstream, how long will it take him (in hours)?

Accepted Answer

Step 1: Find downstream speed of boat: 48 ÷ 3 = 16 km/h. Step 2: Find upstream speed of boat: 48 ÷ 4 = 12 km/h. Step 3: Use formulas: Downstream = b + s, Upstream = b − s, where b = boat speed in still water, s = stream speed. So 16 = b + s and 12 = b − s. Step 4: Adding equations: 28 = 2b, so b = 14 km/h. Step 5: Subtracting: 4 = 2s, so s = 2 km/h. Step 6: Man's speed in still water = boat's speed in still water = 14 km/h (given constant speed in still water). Step 7: Man's downstream speed = 14 + 2 = 16 km/h. Step 8: Time = 48 ÷ 16 = 3 hours.

Question 7

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. A swimmer can swim at a speed equal to the boat's speed in still water. If the swimmer swims downstream for 2 hours and then upstream for 4 hours in the same river, what is the total distance covered by the swimmer?

Accepted Answer

Step 1: Find downstream speed: 48 ÷ 3 = 16 km/h. Step 2: Find upstream speed: 48 ÷ 6 = 8 km/h. Step 3: Using downstream speed = (b + s) and upstream speed = (b − s), where b = boat speed in still water and s = stream speed: b + s = 16 and b − s = 8. Solving: 2b = 24, so b = 12 km/h and s = 4 km/h. Step 4: Swimmer's speed in still water = 12 km/h. Step 5: Swimmer's downstream distance = 12 + 4 = 16 km/h × 2 hours = 32 km. Step 6: Swimmer's upstream distance = 12 − 4 = 8 km/h × 4 hours = 32 km. Step 7: Total distance = 32 + 32 = 64 km.

Question 8

A boat takes 6 hours to travel 120 km downstream and 10 hours to travel the same distance upstream. If the boat must travel 240 km downstream and then immediately return 240 km upstream, what is the total time taken for the entire journey?

Accepted Answer

Step 1: Find downstream speed. Distance = 120 km, Time = 6 hours. Downstream speed = 120/6 = 20 km/h.

Step 2: Find upstream speed. Distance = 120 km, Time = 10 hours. Upstream speed = 120/10 = 12 km/h.

Step 3: Verify boat speed and stream speed. Let boat speed = b, stream speed = s. Then b + s = 20 and b - s = 12. Adding: 2b = 32, so b = 16 km/h and s = 4 km/h. (Check: 16+4=20 ✓ and 16-4=12 ✓)

Step 4: Calculate time for 240 km downstream. Time = 240/20 = 12 hours.

Step 5: Calculate time for 240 km upstream. Time = 240/12 = 20 hours.

Step 6: Total time = 12 + 20 = 32 hours.

Therefore, the answer is 32 hours.

Question 9

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. A man swims at a constant speed in still water. If the man swims the same 48 km downstream, he takes 4 hours. What is the ratio of the man's swimming speed to the boat's speed in still water?

Accepted Answer

Step 1: Find boat's downstream speed = 48/3 = 16 km/h. Step 2: Find boat's upstream speed = 48/6 = 8 km/h. Step 3: Using (b+s) = 16 and (b-s) = 8, solve: b = 12 km/h (boat speed in still water), s = 4 km/h (stream speed). Step 4: Find man's speed in still water. Man goes 48 km downstream in 4 hours, so man's downstream speed = 48/4 = 12 km/h. Step 5: Man's downstream speed = man's speed + stream speed, so 12 = m + 4, thus m = 8 km/h. Step 6: Ratio = man's speed : boat's speed = 8 : 12 = 2 : 3.

Question 10

A boat's speed in still water is 10 km/h and the stream speed is 3 km/h. How long will it take to travel 91 km upstream?

Accepted Answer

Step 1: Upstream speed = Boat speed − Stream speed = 10 − 3 = 7 km/h. Step 2: Time = Distance ÷ Speed = 91 ÷ 7 = 13 hours.

Question 11

A boat's speed in still water is 10 km/h and the stream's speed is 2 km/h. If the boat travels 36 km downstream and then returns to the starting point, what is the total time taken?

Accepted Answer

Step 1: Downstream speed = 10 + 2 = 12 km/h. Step 2: Upstream speed = 10 − 2 = 8 km/h. Step 3: Time downstream = 36 ÷ 12 = 3 hours. Step 4: Time upstream = 36 ÷ 8 = 4.5 hours. Step 5: Total time = 3 + 4.5 = 7.5 hours.

Question 12

A man can row 30 km downstream in 5 hours. The stream speed is 1 km/h. What is his speed in still water?

Accepted Answer

Step 1: Downstream speed = 30 ÷ 5 = 6 km/h. Step 2: Boat speed = Downstream speed − Stream speed = 6 − 1 = 5 km/h.

Question 13

A boat takes 5 hours to travel 60 km upstream. If the boat's speed in still water is 14 km/h, what is the speed of the stream?

Accepted Answer

Step 1: Upstream speed = Distance ÷ Time = 60 ÷ 5 = 12 km/h. Step 2: Upstream speed = Boat speed − Stream speed, so 12 = 14 − Stream speed. Step 3: Stream speed = 14 − 12 = 2 km/h.

Question 14

A boat covers 80 km downstream in 4 hours and the same distance upstream in 5 hours. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 80 ÷ 4 = 20 km/h. Step 2: Upstream speed = 80 ÷ 5 = 16 km/h. Step 3: Stream speed = (Downstream speed − Upstream speed) ÷ 2 = (20 − 16) ÷ 2 = 4 ÷ 2 = 2 km/h.

Question 15

A boat takes 4 hours to travel 60 km downstream and 6 hours to travel the same distance upstream. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 60 ÷ 4 = 15 km/h. Step 2: Upstream speed = 60 ÷ 6 = 10 km/h. Step 3: Stream speed = (Downstream speed − Upstream speed) ÷ 2 = (15 − 10) ÷ 2 = 5 ÷ 2 = 2.5 km/h.

Question 16

The speed of a boat in still water is 9 km/h. It travels 45 km downstream in 3 hours. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = Distance ÷ Time = 45 ÷ 3 = 15 km/h. Step 2: Downstream speed = Boat speed + Stream speed, so 15 = 9 + Stream speed. Step 3: Stream speed = 15 − 9 = 6 km/h.

Question 17

A boat travels 48 km downstream in 3 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = Distance ÷ Time = 48 ÷ 3 = 16 km/h. Step 2: Downstream speed = Boat speed + Stream speed, so 16 = Boat speed + 2. Step 3: Boat speed = 16 − 2 = 14 km/h.

Question 18

A boat's speed in still water is 10 km/h and the stream's speed is 3 km/h. How long will it take the boat to travel 91 km upstream?

Accepted Answer

Step 1: Upstream speed = Boat speed − Stream speed = 10 − 3 = 7 km/h. Step 2: Time = Distance ÷ Speed = 91 ÷ 7 = 13 hours.

Question 19

A man can row a boat at 8 km/h in still water. The stream flows at 3 km/h. How much longer does it take him to row 55 km upstream compared to rowing 55 km downstream?

Accepted Answer

Step 1: Upstream speed = 8 − 3 = 5 km/h. Step 2: Downstream speed = 8 + 3 = 11 km/h. Step 3: Time upstream = 55 ÷ 5 = 11 hours. Step 4: Time downstream = 55 ÷ 11 = 5 hours. Step 5: Difference = 11 − 5 = 6 hours.

Question 20

A boat takes 5 hours to travel 60 km upstream. If the boat's speed in still water is 14 km/h, what is the speed of the stream?

Accepted Answer

Step 1: Upstream speed = Distance ÷ Time = 60 ÷ 5 = 12 km/h. Step 2: Upstream speed = Boat speed − Stream speed, so 12 = 14 − Stream speed. Step 3: Stream speed = 14 − 12 = 2 km/h.

Question 21

A boat travels 60 km downstream in 4 hours and 60 km upstream in 6 hours. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 60 ÷ 4 = 15 km/h. Step 2: Upstream speed = 60 ÷ 6 = 10 km/h. Step 3: Stream speed = (Downstream speed − Upstream speed) ÷ 2 = (15 − 10) ÷ 2 = 5 ÷ 2 = 2.5 km/h.

Question 22

A boat's speed in still water is 9 km/h and the stream speed is 2 km/h. If the boat travels 77 km upstream, how much time does it take?

Accepted Answer

Step 1: Upstream speed = 9 − 2 = 7 km/h. Step 2: Time = 77 ÷ 7 = 11 hours.

Question 23

A man can row 5 km/h in still water. The river flows at 1 km/h. If he rows upstream for 2 hours and then downstream for 2 hours, what is the total distance covered?

Accepted Answer

Step 1: Upstream speed = 5 − 1 = 4 km/h. Distance upstream = 4 × 2 = 8 km. Step 2: Downstream speed = 5 + 1 = 6 km/h. Distance downstream = 6 × 2 = 12 km. Step 3: Total distance = 8 + 12 = 20 km.

Question 24

A boat travels 48 km downstream in 3 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = Distance ÷ Time = 48 ÷ 3 = 16 km/h. Step 2: Downstream speed = Boat speed + Stream speed, so 16 = Boat speed + 2. Step 3: Boat speed = 16 − 2 = 14 km/h.

Question 25

The speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h. How long will it take the boat to travel 72 km downstream and then return to the starting point?

Accepted Answer

Step 1: Downstream speed = 15 + 3 = 18 km/h. Step 2: Upstream speed = 15 - 3 = 12 km/h. Step 3: Time downstream = 72 ÷ 18 = 4 hours. Step 4: Time upstream = 72 ÷ 12 = 6 hours. Step 5: Total time = 4 + 6 = 10 hours.

Question 26

A boat's speed in still water is 10 km/h and the stream speed is 2 km/h. The boat takes 4 hours to travel from point A to point B downstream. How long will it take to return from B to A upstream?

Accepted Answer

Step 1: Downstream speed = 10 + 2 = 12 km/h. Distance AB = 12 × 4 = 48 km. Step 2: Upstream speed = 10 - 2 = 8 km/h. Step 3: Time to return = 48 ÷ 8 = 6 hours.

Question 27

A man rows a boat 30 km downstream and 20 km upstream, taking 4 hours and 5 hours respectively. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 30 ÷ 4 = 7.5 km/h. Step 2: Upstream speed = 20 ÷ 5 = 4 km/h. Step 3: Speed of stream = (Downstream speed − Upstream speed) ÷ 2 = (7.5 − 4) ÷ 2 = 3.5 ÷ 2 = 1.75 km/h. Therefore, the answer is 1.75 km/h.

Question 28

A boat can cover 60 km upstream in 5 hours. If the speed of the stream is 2 km/h, what distance can the boat cover downstream in 3 hours?

Accepted Answer

Step 1: Upstream speed = 60 ÷ 5 = 12 km/h. Step 2: Using upstream speed = boat speed − stream speed: 12 = boat speed − 2, so boat speed = 14 km/h. Step 3: Downstream speed = boat speed + stream speed = 14 + 2 = 16 km/h. Step 4: Distance downstream in 3 hours = 16 × 3 = 48 km. Therefore, the answer is 48 km.

Question 29

The speed of a boat in still water is 15 km/h and the speed of the stream is 3 km/h. How much time will the boat take to cover 72 km downstream and then return to the starting point?

Accepted Answer

Step 1: Downstream speed = 15 + 3 = 18 km/h. Step 2: Upstream speed = 15 − 3 = 12 km/h. Step 3: Time for downstream journey = 72 ÷ 18 = 4 hours. Step 4: Time for upstream journey = 72 ÷ 12 = 6 hours. Step 5: Total time = 4 + 6 = 10 hours. Therefore, the answer is 10 hours.

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