SOLUTION: a motorboat has a constant speed of 14 miles per hour relative to the water going upstream for 33 miles and then returning. the total trip time was 7 hours. use this information to

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Question 559996: a motorboat has a constant speed of 14 miles per hour relative to the water going upstream for 33 miles and then returning. the total trip time was 7 hours. use this information to find the speed of the current.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a motorboat has a constant speed of 14 miles per hour relative to the water going upstream for 33 miles and then returning.
the total trip time was 7 hours. use this information to find the speed of the current.
:
Let c = the rate of the current
then
(14-c) = effective speed upstream (in relation to the land)
and
(14+c) = effective speed downstream
:
Write a time equation; time = dist/speed
:
Time upstr + time downstr = 7 hrs
33%2F%28%2814-c%29%29 + 33%2F%28%2814%2Bc%29%29 = 7
;
Multiply by (14-c)(14+c), results:
33(14+c) + 33(14-c) = 7(14-c)(14+c)
:
462 + 33c + 462 - 33c = 7(196-c^2)
:
924 = 1372 - 7c^2
:
7c^2 = 1372 - 924
:
7c^2 = 448
:
c^2 = 448%2F7
c^2 = 64
c = sqrt%2864%29
c = 8 mph is the speed of the current
:
:
See if this checks out. Find the actual time of each trip.
33/(14-8) = 5.5 hrs
33/(14+8) = 1.5 hrs
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total time: 7.0 hrs