SOLUTION: Jerry rowed upstream against a 2 mile-per-hour current a distance of 12 miles to his camp. He returned rowing downstream later in the day. If the total time first trip was 8 hours,

Question 834068: Jerry rowed upstream against a 2 mile-per-hour current a distance of 12 miles to his camp. He returned rowing downstream later in the day. If the total time first trip was 8 hours, find the time it took rowing for each part of the trip
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Jerry rowed upstream against a 2 mile-per-hour current a distance of 12 miles to his camp.
He returned rowing downstream later in the day.
If the total time for the trip was 8 hours, find the time it took rowing for each part of the trip
:
Let s = rowing speed in still water
If we know his rowing speed in still water, we can find the time each way
:
(s-2) = his effective speed upstream
and
(s+2) = his effective speed downstream
:
Write a time equation, time = dist/speed
time up + time down = 8 hrs
+ = 8
multiply eq by (s-2)(s+2); cancel the denominators and we have
12(s+2) + 12(s-2) = 8(s-2)(s+2)
12s + 24 + 12s - 24 = 8(s^2-4)
24s = 8s^2 - 32
0 = 8s^2 - 24s - 32
simplify, divide by 8
s^2 - 3s - 4 = 0
Factors to
(s-4)(s+1) = 0
the positive solution
s = 4 mph in still water
then
2 mph upstream and 6 mph downstream
Find the times
12/2 = 6 hrs upstream
12/6 - 2 hrs downstream
-----------------------
total time 8 hrs

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