Question

A ship covered 96 km upstream in 32 hours. How long will it take to cover the double distance downstream, if the speed of current is 1/4^th of the speed of ship?
1. 37.2 hrs
2. 28.9 hrs
3. 38.4 hrs
4. 10.2 hrs
5. None of the above/More than one of the above

Answer 1

Correct Answer - Option 3 : 38.4 hrs

Given:

Ship covered 96 km upstream = 32 hours

Speed of current = 1 / 4^th of speed of ship

Formula:

Speed = Distance / Time

If speed of motor boat and stream be x and y km / hr respectively, then

Upstream speed = (x - y) km / hr

Downstream speed = (x + y) km / hr

Calculation:

Let speed of ship in still water be 4x km / hr

Speed of current = 4x × (1 / 4) = x km / hr

According to the question

Upstream speed = 4x – x = 3x

According to the question

3x = 96 / 32

⇒ x = 3 / 3

⇒ x = 1

Downstream speed = 4x + x = 5x = 5 × 1 = 5 km / hr

Double the distance of 96 km = 2 × 96 = 192 km

∴ Time taken by ship to cover 192 km along the current = 192 / 5 = 38.4 hrs