Question

a boat goes 15 km upstream and 10.5 km downstream in 3 hrs 15 min.it goes 12 km upstream and 14 km downstream in 3 hrs.find the speed of the boat

Answer 1

Let speed of river = x km/h
speed of boat = y km/h
∴ downstream = (x + y) km/h
upstream = (y - x) km/h

Case 1 :- boat goes 15 km upstream and 10.5 km downstream in 3 hrs 15 min.
time taken in upstream + time taken in downstream = 3 hrs + 15 min
⇒ 15/(x + y) + 10.5/(y - x) = 3 + 15/60 = 13/4
⇒15/(x + y) + 10.5/(y - x) = 13/4 -------(1)

Case 2 :- boat goes 12 upstream and 14 km downstream in 3hrs .
time taken in upstream + time taken in downstream = 3 hrs
⇒ 12/(x + y) + 14/(y - x) = 3 -----(2)

Solve equations (1) and (2)
4 × equation (1) - 3 × equation (2)
60/(x + y) + 42/(y - x) - 36/(x + y) - 42/(y - x) = 52/4 - 9 = (52 - 36)/4
⇒24/(x + y) = 16/4
⇒ (x + y) = 6 ,put it in equation (1),
(y - x) = 14

Now, (x + y) + (y - x) = 6 + 14
2y = 20 ⇒ y = 10
And x = 4

Hence, speed of boat is 10 km/h