<PRE><B>Question 77959</B>
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/((24+x))}}} = {{{54/((24-x))}}}
:
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</PRE>