A boat can cover 120 km upstream and back in a total of 30 hours, and 25 km upstream and 40 km downstream in a total of 7 hours. How much distance will the boat cover in 16 hours in still water?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 200 km.
Let the speed of the boat be x and the speed of the current be y
So,
Downstream speed = x + y and, Upstream speed = x - y
We know that,
Speed = Distance/Time
⇒ 120/(x + y) + 120/(x - y) = 30.......(1) and,
⇒ 40/(x + y) + 25/(x - y) = 7........(2)
On multiplying equation 2 by 3 and subtracting from eq 1 we get,
⇒ 120/(x + y) + 120/(x - y) - 120/(x + y) - 75/(x - y) = 30 - 21
⇒ 120/(x - y) - 75/(x - y) = 9
⇒ 45/(x - y) = 9
⇒ (x - y) = 5.........(3)
On putting eq 3 in eq 2 we get,
⇒ 40/(x + y) + 25/5 = 7
⇒ 40/(x + y) + 5 = 7
⇒ 40/(x + y) = 2
⇒ (x + y) = 20.......(4)
Solving eq 3 and 4
⇒ 2x = 25
⇒ x = 12.5
Thus, the speed of the boat = x = 12.5
Distance covered in 16 hours
Distance = 16 × 12.5 = 200 km