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

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) (Show Source): You can put this solution on YOUR website!
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
:
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
:
Dist downstream = dist upstream
(16+x) = (16-x)
:
Get rid of the denominators, multiply equation by 12, results:
3(16 + x) = 4(16 - x)
:
48 + 3x = 64 - 4x
:
3x + 4x = 64 - 48
:
7x = 16
:
x = 16/7 is the speed to the current
:
That's about 2.3 mph
:
:
Check solution by finding the distances
1/4(16+2.3) = 4.6 mi
1/3(16-2.3) = 4.6 mi
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