It takes 32 hours for a motorboat moving downriver to get from pier A to pier B. The return journey takes 48 hours. How long does it take an unpowered raft to cover this distance?A

of his route and an additional 40 miles. He has yet to cover 118 miles less than 0.75 of his route. How long is his route?

Boat problem:

Let x = distance from pier A to pier B

Let SD = speed of boat downstream

Let SU = speed of boat upstream

Then, speed of current SC is

SD - SU = SC

x/32 = SD

x/48 = SU

(SC)(t) = x

(x/32 - x/48)t = x

(1/32 - 1/48)t = 1

(3/96 - 2/96)t = 1

1/96t = 1

t = 96 hours

Bicyclist problem:

Let R = Route distance

Then,

5/7R + 40 + 118 - 3/4R = R

R + 3/4R -5/7R = 158

R + 1/28R = 158

29/28R = 158

R = 152.55 miles

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