<PRE><B>Question 266575</B>
A motorboat can maintain a constant speed of 16 miles per hour relative to the water. 
The boat makes a trip upstream to a certain point in 20 minutes, the return trip takes 15 minutes. 
What is the speed of the current?
:
Change 20 min to {{{1/3}}} hr
Change 15 min to {{{1/4}}} hr
:
Let c = rate of the current
then
(16-c) = rate upstream
and
(16+c) = rate downstream
:
Assume the trip up and the trip back were the same distance
Write a distance equation: dist = time * rate
:
Dist upstream = dist downstream
{{{1/4}}}(16+c) = {{{1/3}}}(16-c)
Multiply both sides by 12, to get rid of the denominators, results:
3(16+c) = 4(16-c)
48 + 3c = 64 - 4c
3c + 4c = 64 - 48
7c = 16
c = {{{16/7}}}
c = 2.2857 mph is the current
:
:
Check solution by finding the distance of each trip (should be equal)
.25(16+2.2857) = 4.57 mi
.333(16-2.2857) = 4.57 mi</PRE>