Question

The time taken by a boat to travel upstream to a certain distance and return back is 14 hours. If the velocity of boat in still water is 35 kmh$ ^{-1} $ and velocity of the stream is 5 kmh$ ^{-1} $, the distance travelled by the boat before it returns is

• A. 100 km
• B. 240 km
• C. 120 km
• D. 180 km

Hint:

Remember to account for the stream's velocity when calculating the effective speed of the boat.

Answer 1

The Correct Option is B

Step 1: Define variables.
Distance = $ d $
Boat speed in still water $ v_b = 35 $ kmh$ ^{-1} $
Stream speed $ v_s = 5 $ kmh$ ^{-1} $
Total time $ t = 14 $ hours

Step 2: Calculate upstream and downstream speeds.
Upstream speed $ v_{up} = v_b - v_s = 30 $ kmh$ ^{-1} $
Downstream speed $ v_{down} = v_b + v_s = 40 $ kmh$ ^{-1} $
Step 3: Express time for upstream and downstream travel.
Time upstream $ t_{up} = d / v_{up} = d / 30 $
Time downstream $ t_{down} = d / v_{down} = d / 40 $
Step 4: Use total time.
$ t_{up} + t_{down} = 14 $
$ \frac{d}{30} + \frac{d}{40} = 14 $
Step 5: Solve for $ d $.
$ \frac{4d + 3d}{120} = 14 $
$ \frac{7d}{120} = 14 $
$ 7d = 14 \times 120 $
$ d = 2 \times 120 = 240 $ km
Step 6: Conclusion.
The distance travelled upstream (before returning) is 240 km.