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Algebra
Tutor: None Selected Time limit: 1 Day







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

A bicyclist covered 
5
7

 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?



Apr 4th, 2015

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

Apr 4th, 2015

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