SOLUTION: The speed of a boat in still water is 24mph. If the boat travels 54 miles upstream in the same time that it takes to travel 90 miles downstream, find the speed of the current.

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Question 77959This question is from textbook Intermediate Algebra
: The speed of a boat in still water is 24mph. If the boat travels 54 miles upstream in the same time that it takes to travel 90 miles downstream, find the speed of the current. This question is from textbook Intermediate Algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The speed of a boat in still water is 24 mph. If the boat travels 54 miles upstream in the same time that it takes to travel 90 miles downstream, find the speed of the current.
:
Let x = the speed of the current
:
Then:
Speed up-stream = (24-x)
Speed down-stream = (24-x)
:
Write a time equation, Time = distance/speed:
Time to go 54 mi = time to go 90 mi
90%2F%28%2824%2Bx%29%29 = 54%2F%28%2824-x%29%29
:
Cross multiply
:
54(24+x) = 90(24-x)
:
1296 + 54x = 2160 - 90x
:
54x + 90x = 2460 - 1296
:
144x = 864
:
x = 864/144
:
x = 6 mph is the current
:
:
Check the solution using the time:
90/30 = 3hrs
54/18 = 3hrs also