Question

A ship travels downstream for 36 miles and then makes the same return trip upstream. The trip downstream took 3/4 of an hour less then the trip upstream.

If the rate of the current is 4mph
find the rate of the ship in still water and the time it takes to complete each part of the trip.

Answer 1

speed down = s + 4
speed up = s - 4

time down = t
time up = t + .75

(s+4)(t) =36 so t = 36/(s+4)

(s-4)([36/(s+4)]+.75) = 36

36(s-4)/(s+4) +.75(s-4) = 36
36(s-4) +.75 (s^2-16) = 36(s+4)
.75 s^2 -12 -36(8) = 0
(3/4) s^2 = 4*25*3
s^2 = 4*4 *25
s = 4*5
s = 20
*****************************************
check
speed down = 24
time down = 36/24 = 6/4 = t
speed up = 16
time up = 36/16 = 9/4
9/4 - 6/4 = 3/4 sure enough

Answer 2

Thanks Damon, you just beat be to the correction of this earlier post.

https://www.jiskha.com/questions/1753073/A-ship-travels-downstream-for-36-miles-and-then-makes-the-same-return-trip-upstream

Answer 3

Whew :)