<PRE><B>Question 142033</B>
he speed of a stream is 6 mph. If a boat travels 98 miles downstream in the same time that it takes to travel 49 miles upstream, what is the speed of the boat in still water?
:
Let s = speed in still water
then
(s-6) = speed upstream (in relation to the land)
and
(s+6) = speed downstream
:
Write a time equation: Time = dist/speed
:
Time downstream = time upstream
{{{98/(s+6)}}} = {{{49/(s-6)}}}
Cross multiply
98(s-6) = 49(s+6)
:
98s - 588 = 49s + 294
:
98s - 49s = 294 + 588
:
49s = 882
s = {{{882/49}}}
s = 18 mph in still water
:
:
Check solution by finding out if the times are equal
12 mph = speed up
24 mph = speed down
49/12 = 4.0833
98/24 = 4.0833

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