SOLUTION: Marine travel. Sandy's tugboat moves at a rate of 10 mph in still water. It travels 24 miles upstream and 24 miles downstream in a total time of 5 hours. What is the speed of th

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Question 79144This question is from textbook
: Marine travel. Sandy's tugboat moves at a rate of 10 mph in still water. It travels 24 miles upstream and 24 miles downstream in a total time of 5 hours. What is the speed of the current? This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source):
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Marine travel. Sandy's tugboat moves at a rate of 10 mph in still water. It travels 24 miles upstream and 24 miles downstream in a total time of 5 hours. What is the speed of the current?
:
Let c = speed of the current:
Then:
Speed upstream = (10-c)
Speed downstream = (10+c)
:
Time = Distance/Speed
:
Time upstream + Time downstream = 5 hrs
+ = 5
:
Multiply equation by (10-c)(10+c); get rid of the denominators:
24(10+c) + 24(10-c) = 5(10+c)(10-c)
:
240 + 24c + 240 - 24x = 5(100 - c^2)
480 = 500 - 5c^2
5c^2 = 500 - 480
5c^2 = 20
c^2 = 20/5
c = Sqrt(4))
c = 2 mph is the current
:
:
Check by finding the times, upstream & down stream
24/(10-2) = 3 hrs
24/(10+2) = 2 hrs
Total time= 5 hrs