Question

2 hour 40 min after a raft left pier A and traveled downstream, a motorboat left pier B and traveled upstream toward the raft. The two met 27 km away from B. Find the speed of the raft if the speed of the motorboat in still water is 12 km/hour and the distance from A to B is 44 km.

Answer 1

If the boat went 27 km, the raft went 17 km when they met.
let the speed of the current (as well as the raft) be x km/h
then the speed of the boat going upstream is 12-x km/h
time taken by the raft = 17/x
time taken by the boat = 27/(12-x)
The difference in their times = 2 2/3 hrs = 8/3 hrs

17/x - 27/(12-x) = 8/3
times 3x(12-x)
51(12-x) - 81x = 8x(12-x)
612 - 51x - 81x = 96x - 8x^2
8x^2 - 228x + 612 = 0
divide by 4
2x^2 - 57x + 153 = 0
(x-3)(2x - 51) = 0
x = 3 or x = 51/2, but x < 12 or else the boat would be going backwards.

the speed of the raft or the speed of the current is 3 km/h

Answer 2

This answer is right!

Answer 3

wow good job with that explanation

Answer 4

Thanks for helping me in RSM