Question 1

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 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 and 32 km upstream in 8 hours. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 36 ÷ 4 = 9 km/h. Step 2: Upstream speed = 32 ÷ 8 = 4 km/h. Step 3: Stream speed = (Downstream speed − Upstream speed) ÷ 2 = (9 − 4) ÷ 2 = 5 ÷ 2 = 2.5 km/h.

Question 4

A boat takes 5 hours to travel 60 km downstream. If the boat's speed in still water is 11 km/h, what is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 60 ÷ 5 = 12 km/h. Step 2: Downstream speed = Boat speed + Stream speed, so 12 = 11 + Stream speed. Step 3: Stream speed = 12 − 11 = 1 km/h.

Question 5

A boat travels 80 km upstream in 10 hours. If the stream's speed is 2 km/h, what is the boat's speed in still water?

Accepted Answer

Step 1: Upstream speed = 80 ÷ 10 = 8 km/h. Step 2: Upstream speed = Boat speed − Stream speed, so 8 = Boat speed − 2. Step 3: Boat speed = 8 + 2 = 10 km/h.

Question 6

A boatman rows 24 km downstream and 16 km upstream, taking 4 hours for the entire journey. If the stream's speed is 2 km/h, what is the boat's speed in still water?

Accepted Answer

Step 1: Let boat speed = b km/h. Downstream speed = b + 2, Upstream speed = b − 2. Step 2: Time equation: 24/(b+2) + 16/(b−2) = 4. Step 3: Multiply through: 24(b−2) + 16(b+2) = 4(b+2)(b−2). Step 4: 24b − 48 + 16b + 32 = 4(b² − 4). Step 5: 40b − 16 = 4b² − 16. Step 6: 40b = 4b². Step 7: 10b = b². Step 8: b = 10 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 much time will the boat take 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 boat can travel 35 km upstream in 5 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: Upstream speed = 35/5 = 7 km/h. Step 2: Upstream speed = Boat speed - Stream speed. Step 3: 7 = Boat speed - 2. Step 4: Boat speed = 7 + 2 = 9 km/h.

Question 10

A boat's speed in still water is 20 km/h. It travels 60 km downstream and 40 km upstream, taking a total of 5 hours. What is the speed of the stream?

Accepted Answer

Step 1: Let stream speed = s km/h. Step 2: Downstream speed = 20 + s, Upstream speed = 20 - s. Step 3: Time equation: 60/(20+s) + 40/(20-s) = 5. Step 4: 60(20-s) + 40(20+s) = 5(20+s)(20-s). Step 5: 1200 - 60s + 800 + 40s = 5(400 - s²). Step 6: 2000 - 20s = 2000 - 5s². Step 7: 5s² - 20s = 0. Step 8: 5s(s - 4) = 0. Step 9: s = 4 km/h (s ≠ 0).

Question 11

A man can row a boat at 8 km/h in still water. He rows upstream for 2 hours and then downstream for 1.5 hours. If the total distance covered is 20 km, what is the speed of the stream?

Accepted Answer

Step 1: Let stream speed = s km/h. Step 2: Upstream speed = 8 - s, Downstream speed = 8 + s. Step 3: Distance upstream = (8-s) × 2 = 16 - 2s. Step 4: Distance downstream = (8+s) × 1.5 = 12 + 1.5s. Step 5: Total distance: (16 - 2s) + (12 + 1.5s) = 20. Step 6: 28 - 0.5s = 20. Step 7: 0.5s = 8. Step 8: s = 4 km/h.

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