The speed of a boat in still water is 10 km/h. The time taken by the boat to go 35 km downstream is 1.25 times the time taken by it to go 14 km upstream. How much time (in hours) will it take to go 60 km downstream?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 4.5.
Given:
The speed of a boat in still water is 10 km/h.
The time taken by the boat to go 35 km downstream is 1.25 times the time taken by it to go 14 km upstream
Formula used:
Speed = distance/time
Upstream speed = Speed of a boat in still water (x) - Speed of the current (y)
Downstream speed = Speed of a boat in still water (x) + Speed of the current (y)
Calculations:
According to the question:
⇒ 35/(10 + y) = 1.25 × 14/(10 - y)
⇒ 5/(10 + y) = 1.25 × 2/(10 - y)
⇒ (10 - y) = .25 × 2 × (10 + y)
⇒ (10 - y) = 5 + .5y
⇒ 1.5y = 5
⇒ y = 10/3
So,
Downstream speed = 10 + 10/3 = 40/3
And
Required time taken = 60/(40/3) = 4.5 hours