SOLUTION: a motor boat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 min

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Question 96312: a motor boat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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a motor boat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current?
:
Let x = speed of the current
:
(16 + x) = speed downstream
(16 - x) = speed upstream
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Convert 20 min to hrs: 20/60 = 1/3 hr
Convert 15 min to hrs: 15/60 = 1/4 hr
:
We know the distance upstream and distance downstream are equal
Make a distance equation from that fact: Dist = time * speed
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Dist downstream = dist upstream
1%2F4(16+x) = 1%2F3(16-x)
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Get rid of the denominators, multiply equation by 12, results:
3(16 + x) = 4(16 - x)
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48 + 3x = 64 - 4x
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3x + 4x = 64 - 48
:
7x = 16
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x = 16/7 is the speed to the current
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That's about 2.3 mph
:
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Check solution by finding the distances
1/4(16+2.3) = 4.6 mi
1/3(16-2.3) = 4.6 mi