Question 1

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 2

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 3

A man can row 36 km downstream in 4 hours. The speed of the current is 1.5 km/h. What is his speed upstream?

Accepted Answer

Step 1: Downstream speed = 36 ÷ 4 = 9 km/h. Step 2: Boat speed = Downstream speed − Current speed = 9 − 1.5 = 7.5 km/h. Step 3: Upstream speed = Boat speed − Current speed = 7.5 − 1.5 = 6 km/h.

Question 4

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

Accepted Answer

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

Question 5

The speed of a boat in still water is 12 km/h. If it takes 6 hours to travel 60 km upstream, what is the speed of the stream?

Accepted Answer

Step 1: Upstream speed = Distance ÷ Time = 60 ÷ 6 = 10 km/h. Step 2: Upstream speed = Boat speed − Stream speed, so 10 = 12 − Stream speed. Step 3: Stream speed = 12 − 10 = 2 km/h.

Question 6

A boat covers 72 km downstream in 6 hours and 60 km upstream in 6 hours. What is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = 72 ÷ 6 = 12 km/h. Step 2: Upstream speed = 60 ÷ 6 = 10 km/h. Step 3: Boat speed = (Downstream + Upstream) ÷ 2 = (12 + 10) ÷ 2 = 22 ÷ 2 = 11 km/h.

Question 7

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.

Question 8

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 9

A man can row 30 km downstream in 5 hours. If the stream's speed is 2 km/h, what is the speed of the man in still water?

Accepted Answer

Step 1: Downstream speed = 30 ÷ 5 = 6 km/h. Step 2: Downstream speed = Boat speed + Stream speed. Step 3: 6 = Boat speed + 2. Step 4: Boat speed = 6 - 2 = 4 km/h.

Question 10

A boat takes 4 hours to travel 60 km upstream. If the boat's speed in still water is 18 km/h, what is the speed of the stream?

Accepted Answer

Step 1: Upstream speed = 60 ÷ 4 = 15 km/h. Step 2: Upstream speed = Boat speed - Stream speed. Step 3: 15 = 18 - Stream speed. Step 4: Stream speed = 18 - 15 = 3 km/h.

Question 11

A boat covers 84 km downstream in 6 hours and the same distance upstream in 7 hours. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 84 ÷ 6 = 14 km/h. Step 2: Upstream speed = 84 ÷ 7 = 12 km/h. Step 3: Stream speed = (Downstream speed - Upstream speed) ÷ 2 = (14 - 12) ÷ 2 = 2 ÷ 2 = 1 km/h.

Question 12

A boatman can row 24 km downstream in 2 hours. The ratio of his speed in still water to the stream's speed is 3:1. If he rows upstream for 3 hours and then downstream for 2 hours, what is the total distance covered?

Accepted Answer

Step 1: Downstream speed = 24/2 = 12 km/h. Step 2: Let boat speed = 3x, stream speed = x. Then 3x + x = 12 → 4x = 12 → x = 3. Step 3: Boat speed = 9 km/h, stream speed = 3 km/h. Step 4: Upstream speed = 9 - 3 = 6 km/h. Step 5: Distance upstream in 3 hours = 6 × 3 = 18 km. Step 6: Distance downstream in 2 hours = 12 × 2 = 24 km. Step 7: Total distance = 18 + 24 = 42 km.

Question 13

A boat can travel 120 km downstream in the same time it takes to travel 80 km upstream. The boat's speed in still water is 25 km/h. What is the speed of the stream?

Accepted Answer

Step 1: Let stream speed = s km/h. Downstream speed = 25 + s, Upstream speed = 25 - s. Step 2: Time is equal, so 120/(25+s) = 80/(25-s). Step 3: Cross multiply: 120(25-s) = 80(25+s). Step 4: 3000 - 120s = 2000 + 80s. Step 5: 1000 = 200s. Step 6: s = 5 km/h.

Question 14

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, how long will it take him if his swimming speed is half the boat's speed in still water?

Accepted Answer

Step 1: Let boat speed in still water = b km/h, stream speed = s km/h. Downstream: (b+s) = 48/3 = 16 km/h. Upstream: (b-s) = 48/6 = 8 km/h. Step 2: Solving: b = 12 km/h, s = 4 km/h. Step 3: Man's speed in still water = 12/2 = 6 km/h. Step 4: Man's downstream speed = 6 + 4 = 10 km/h. Step 5: Time = 48/10 = 4.8 hours.

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