Question

A person rows a distance of 20 km upstream and 15 km downstream in a total time of \(2 \frac{5}{12}\) hours. If the speed of the current is 4 km/h, then in how many hours can he row a distance of 64 km upstream?
1. \(5 \frac{1}{3}\)
2. \(4\frac{2}{3}\)
3. \(5\frac{1}{2}\)
4. \(4\frac{1}{4}\)

Answer 1

Correct Answer - Option 1 : \(5 \frac{1}{3}\)

Given:

A person rows a distance of 20 km upstream and 15 km downstream in a total time of 2(5/12) hours 

Speed of the current is 4 km/h 

Formula used:

Distance = speed × time 

Speed in downstream = speed of the boat + speed of the stream 

Speed in upstream = speed of the boat - the speed of the stream 

Calculation:

Let the speed of the boat be 'x' km/h 

Speed in downstream = x + 4  km/h 

Speed in upstream = x - 4 km/h 

Now ,

Time taken in downstream = 15/(x + 4) hours 

Time taken in upstream = 20/(x - 4)  hours 

Total time = time of upstream + time of downstream 

⇒ 2(5/12) = [15 /(x + 4)] + [20/(x - 4)]

⇒ x = 16 

Now time taken to cover 64 km in upstream 

Time = 64/(x -4) 

⇒ 64(/16 - 4) = 64/12 

⇒ 16/3 hours 

∴ Boat will take 16/3 hours to complete 64 km in upstream.