<PRE><B>Question 138852</B>
A boat travels 100 miles downstream in the same length of time it travels 50 miles upstream. if the boat&#39;s speed in still water is 30 mph, find the speed of the current river.
:
Let x = speed of the current:
:
(30-x) = speed upstream
(30+x) = speed down stream
;
the times of the two trips are given as equal: 
write a time equation: Time = dist/speed 
;
{{{100/((30+x))}}} = {{{50/((30-x))}}}
Cross multiply:
50(30+x) = 100(30-x)
:
1500 + 50x = 3000 - 100x
:
50x + 100x = 3000 - 1500
:
150x = 1500
x = {{{1500/150}}}
x = 10 mph is the speed of the current:
:
:
Check solution by finding the times of each trip:
100/40 = 2.5 hrs
50/20 = 2.5 hrs
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