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Question

A boat sails 40 km downstream and then 40 km upstream in a river. The boat's speed in still water is 12 km/hr and the speed of the stream is 4 km/hr. How much time does the boat take to cover the entire distance (both upstream and downstream)?

This question was previously asked in
RRB ALP 2025 CBT 2 Wiremen Question Paper (28-Jul-2026) (Shift 2)
The correct answer is

7.5 hours

To determine how much time the boat takes to cover the entire distance of 40 km downstream and 40 km upstream, we need to calculate the time taken for each journey and then sum these times. Here's the step-by-step solution:

  1. Calculate the downstream speed: The speed of the boat in still water is 12 km/hr, and the speed of the stream is 4 km/hr. The downstream speed is the sum of the boat's speed and the stream's speed.

\(v_{\text{downstream}} = v_{\text{boat}} + v_{\text{stream}} = 12 \,\text{km/hr} + 4 \,\text{km/hr} = 16 \,\text{km/hr}\)

  1. Calculate the time taken to travel downstream: The downstream distance is 40 km. Time is calculated using the formula:

\(t_{\text{downstream}} = \frac{\text{distance}}{\text{speed}} = \frac{40 \,\text{km}}{16 \,\text{km/hr}} = 2.5 \,\text{hours}\)

  1. Calculate the upstream speed: The upstream speed is the difference between the boat's speed and the stream's speed.

\(v_{\text{upstream}} = v_{\text{boat}} - v_{\text{stream}} = 12 \,\text{km/hr} - 4 \,\text{km/hr} = 8 \,\text{km/hr}\)

  1. Calculate the time taken to travel upstream: The upstream distance is 40 km.

\(t_{\text{upstream}} = \frac{\text{distance}}{\text{speed}} = \frac{40 \,\text{km}}{8 \,\text{km/hr}} = 5 \,\text{hours}\)

  1. Calculate the total time for the round trip: Add the times for both the downstream and upstream journeys.

\(t_{\text{total}} = t_{\text{downstream}} + t_{\text{upstream}} = 2.5 \,\text{hours} + 5 \,\text{hours} = 7.5 \,\text{hours}\)

Therefore, the total time taken for the boat to cover the entire journey, both upstream and downstream, is 7.5 hours.

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Similar Questions

  1. To go a certain distance of 40 km upstream a rower takes 8 hours while it takes her only 5 hours to row the same distance downstream. What was the rower’s speed in still water?


Important Questions from Boat and River

  1. A boat sails 15 km of a river towards upstream in 5 hours. How long (in hours) will it take to cover the same distance downstream, if the speed of river is one-fourth the speed of the boat in still water?

  2. The speed of boat upstream is 5 kmph. Its speed in still water is 10 kmph. How many minutes will it take to row 25 km downstream?

  3. Sudha can travel a certain distance downstream in 6 hours by boat and return to the starting point in 9 hours. If the stream flows at a speed of 3 km/h, how long (in hours) will it take to cover a distance of 67.5 km in still water?

  4. The downstream speed of a boat is 20 km/hr and the speed of stream is 4 km/hr. What will be the total time taken by the boat to cover 160 km downstream and 96 km upstream?

  5. A man covered a distance of 18 km in 3 hours, 7.2 km in 2 hours and 15 km in 5 hours. What is the average distance traveled by him per hour?

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