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

3 km/h

Explanation:

Let c represent the speed of the current in km/h, and t the time in hours after the raft leaves point A. 2 hours 40 minutes is 8/3 hours.

Distance = Speed × Time

The watercraft meet at a point 27 km upstream from B, so we have two equations involving these variables:

27 = 44 - ct

27 = (12-c)(t -8/3)

Equating these two versions of "27", we have ...

44 -ct = 12t -32 -ct +(8/3)c

76 = 12t + 8/3·c . . . . . add 32+ct

9t +2c = 57 . . . . multiply by 3/4

t = (57 -2c)/9 . . . .solve for t

Now, we can substitute this into the first of the above equations, after rearranging it to ...

ct = 17

c(57 -2c)/9 = 17

2c^2 -57c +153 = 0 . . . . multiply by 9, subtract the left side

c = (57-√((-57)^2 -4(2)(153)))/(2·2) = (57 -√2025)/4 = 12/4 . . . . quadratic formula

c = 3

The speed of the current is 3 km/h.