Brooke A.

asked • 04/04/17

Help??? Im so confused

A boat traveled 160 miles downstream and back. The trip downstream took 8 hours. The trip back took 16 hours. What is the speed of the boat in still water? What is the speed in the current?

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Inactive Tutor answered • 04/04/17

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Edited solution provided in Comments window below.

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I put the solution in this comment because of difficulties editing in the the ANSWER window.
 
v = speed in still water 
w = speed of current
u = speed in current
 
Downstream:
 
8(v + w) = 160/2 = 80 ⇒ v + w = 10
 
Upstream:
 
16(v - w) = 160/2 = 80 ⇒ v - w = 5
 
Solve this system of equations:
 
v + w = 10
v - w = 5
 
Add the 2 equations and get 
 
2v = 15
v = 15/2 = 7.5 miles/hour
 
From first equation and v = 7.5 get
 
7.5 + w = 10
w = 10 - 7.5 = 2.5 miles/hour
 
u = v - w = 7.5 - 2.5 = 5 miles/hour
 
You can test the solutions.
 
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04/04/17

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