SOLUTION: Suppose a boat travels 30 miles downstream when the current is 3 mph, then travels 30 miles upstream against a 2 mph current. If the total travel time is 5 hours, what is the speed
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Question 312899: Suppose a boat travels 30 miles downstream when the current is 3 mph, then travels 30 miles upstream against a 2 mph current. If the total travel time is 5 hours, what is the speed of the boat in still water? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Suppose a boat travels 30 miles downstream when the current is 3 mph,
then travels 30 miles upstream against a 2 mph current.
If the total travel time is 5 hours, what is the speed of the boat in still water?
:
Let s = boat speed in still water
then
(s+3) = speed downstream
and
(s-2) = speed upstream
:
Write a time equation: time = dist/speed
:
down time + up time = 5 hrs + = 5
Multiply by (s+3)(s-2), results
30(s-2) + 30(s+3) = 5(s+3)(s-2)
:
30s - 60 + 30s + 90 = 5(s^2 + s - 6)
:
60s + 30 = 5s^2 + 5s - 30
Combine on the right
0 = 5s^2 + 5s - 60s - 30 - 30
:
5s^2 - 55s - 60 = 0
Simplify, divide by 5
s^2 - 11s - 12 = 0
Factor
(s-12)(s+1) = 0
positive solution
s = 12 mph in still water
:
:
Check solution by finding the times
30/(12+3) = 2 hrs
30/(12-2) = 3 hrs
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total time: 5 hrs
