SOLUTION: A boat heads upstream a distance of 30 miles on the Mississippi river, whose current is running at 5 miles per hour. If the trip back takes an hour less, what was the speed of the

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Question 159972: A boat heads upstream a distance of 30 miles on the Mississippi river, whose current is running at 5 miles per hour. If the trip back takes an hour less, what was the speed of the boat in still water?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A boat heads upstream a distance of 30 miles on the Mississippi river, whose
current is running at 5 miles per hour. If the trip back takes an hour less,
what was the speed of the boat in still water?
:
Let s = speed of the boat in still water
then
(s-5) = speed upstream
and
(s+5) = speed downstream
:
:
Write a time equation: Time = dist%2Fspeed
:
Time up = time down - 1 hr
30%2F%28%28s-5%29%29 = 30%2F%28%28s%2B5%29%29 + 1
:
Multiply equation by (s+5)(s-5); results:
30(s+5) = 30(s-5) + (s+5)(s-5)
:
30s + 150 = 30s - 150 + (s^2-25)
:
Combine like terms on the right
0 = s^2 + 30s - 30s - 25 - 150 - 150
:
0 = s^2 - 325
:
s^2 = +325
s = sqrt%28325%29
s = 18 mph boat speed in still water
:
:
Check solution by finding the time for each
30/13 = 2.3 hr
30/23 = 1.3 hr
----------------
differ = 1 hr