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A boat travels 50 km upstream and 70 km downstream in a total time of 10 hours.

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Question: A boat travels 50 km upstream and 70 km downstream in a total time of 10 hours. If the speed of the boat in still water is 15 km/h, what is the speed of the current?

Options:

  1. 2 km/h
  2. 3 km/h
  3. 4 km/h
  4. 5 km/h

Correct Answer: 4 km/h

Solution: 

Let the speed of current be x km/h. Time upstream = 50/(15-x) and time downstream = 70/(15+x). Setting up the equation: 50/(15-x) + 70/(15+x) = 10.

A boat travels 50 km upstream and 70 km downstream in a total time of 10 hours.

Practice Questions

Q1
A boat travels 50 km upstream and 70 km downstream in a total time of 10 hours. If the speed of the boat in still water is 15 km/h, what is the speed of the current?
  1. 2 km/h
  2. 3 km/h
  3. 4 km/h
  4. 5 km/h

Questions & Step-by-Step Solutions

A boat travels 50 km upstream and 70 km downstream in a total time of 10 hours. If the speed of the boat in still water is 15 km/h, what is the speed of the current?
  • Step 1: Understand the problem. A boat travels upstream (against the current) and downstream (with the current). We need to find the speed of the current.
  • Step 2: Define the variables. Let the speed of the current be 'x' km/h.
  • Step 3: Determine the speed of the boat upstream. The speed of the boat upstream is the speed in still water minus the speed of the current: 15 - x km/h.
  • Step 4: Determine the speed of the boat downstream. The speed of the boat downstream is the speed in still water plus the speed of the current: 15 + x km/h.
  • Step 5: Calculate the time taken to travel upstream. Time upstream = distance upstream / speed upstream = 50 / (15 - x) hours.
  • Step 6: Calculate the time taken to travel downstream. Time downstream = distance downstream / speed downstream = 70 / (15 + x) hours.
  • Step 7: Set up the equation for total time. The total time for both trips is 10 hours, so we write the equation: 50 / (15 - x) + 70 / (15 + x) = 10.
  • Step 8: Solve the equation for 'x'. This will give us the speed of the current.
  • Relative Speed – Understanding how the speed of the boat and the current affect the effective speed when traveling upstream and downstream.
  • Time Calculation – Using the formula time = distance/speed to set up equations for total travel time.
  • Algebraic Manipulation – Solving equations involving fractions to find the unknown variable (speed of the current).
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