college algebra word problems

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i am stuck on the following problem. here is a pic of the problem

any help would be appreciated

Oct 20th, 2017

We know the distance formula; d = rt
where, d = distance; r = rate; t = time
Solving for time (t) => t = d/r

Let x = speed of current
t1 =Time going downstream = 120/(18+x)
t2 =Time going upstream = 24/(18-x)

Since the boat travels 120 miles downstream in the same time it travels 8 miles upstream we can set t1 and t2 equal to each other and solve for x.
120/(18+x) = 24/(18-x) 
Cross mulitply and we have: 120(18-x) = 24(18+x)
Simplify by dividing both sides by 24:  5(18-x) = (18+x)
90 - 5x = 18 + x => 90 = 18 + 6x => 72 = 6x => x =12
Therefore, Speed of current = 12 mph

Hope this helps, and if it does don't forget to "best" my answer! :)

Dec 3rd, 2014

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