A power boat travels down a river from A to B, atfull throttle. The trip takes 3

Question

A power boat travels down a river from A to B, atfull throttle. The trip takes 3.0h. The boat then heads back to point B, again at full throttle.The time, the trip takes 15h. With no gas left, the boat drifts with a steady current backto point B. How long does the third trip take? Please show steps! :) A power boat travels down a river from A to B, atfull throttle. The trip takes 3.0h. The boat then heads back to point B, again at full throttle.The time, the trip takes 15h. With no gas left, the boat drifts with a steady current backto point B. How long does the third trip take? Please show steps! :)

Explanation / Answer

First, set up equations for the given information: -- Let V(c) = Velocity of the current Let V(b) = Velocity of the boat D = distance travelled ----> just for purposes ofgenerating equations -- From point A--->B D = [V(c) + V(b)]*3 ----> eq 1 -- From B --->A -D = [V(c) - V(b)]*15 ---> eq 2 -- From A--->B (floating) D = V(c)*T ---> eq 3 -- -- Multiply eq 2 through by -1 and we get: D = [V(b) - V(c)]*15 ----> eq 2A -- -- Set eq 1 and eq 2A equal to each other, and solve forV(c): [V(c) + V(b)]*3 = [V(b) - V(c)]*15 3V(c) + 3V(b) = 15V(b) - 15V(c) 18V(c) = 12V(b) V(c) = (2/3)V(b) -- -- Next, we'll set eq 3 and eq 1 equal to each other: V(c)*T = [V(c) + V(b)]*3 -- substitute for V(c) what we found earlier: -- (2/3)V(b)*T = [(2/3)V(b) + V(b)]*3 (2/3)V(b)*T = 2V(b) + 3 V(b) T = 5V(b) / (2/3)V(b) T = 15/2 T = 7.5 hours -- -- Hope this helps.

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