SOLUTION: A motorboat moves 12 mph in still water. it travels 45 mi upstream and 45 mi downstream in a total time of 8.0 hrs. what is the speed if the current?

Question 925376: A motorboat moves 12 mph in still water. it travels 45 mi upstream and 45 mi downstream in a total time of 8.0 hrs. what is the speed if the current?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = speed of current
s = d/t
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up:
12 + x = 45/tu
tu = 45/(12 + x)
---
down:
12 - x = 45/td
td = 45/(12 - x)
---
tu + td = 8 = 45/(12 + x) + 45/(12 - x)
8 = 45(12 - x)/(12 - x)(12 + x) + 45(12 + x)/(12 - x)(12 + x)
8 = ( 45(12 - x) + 45(12 + x) )/(12 - x)(12 + x)
8 = ( 540 - 45x + 540 + 45x )/(144 - xx)
8 = 1080/(144 - xx)
8(144 - xx) = 1080
1152 - 8xx = 1080
8xx = 1152 - 1080
xx = (1152 - 1080)/8
xx = 9
x = 3
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answer:
x = speed of current = 3 mph
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