SOLUTION: A river has a current of 5mph. It takes Al half an hour longer to paddle upstream 1.2 miles than to paddle downstream the same distance. What is Al's rate in still water.
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Question 465553: A river has a current of 5mph. It takes Al half an hour longer to paddle upstream 1.2 miles than to paddle downstream the same distance. What is Al's rate in still water.
Setting word problems up always seems to be more difficult than setting them up. I need to find a quadratic equation then solve with this problem.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A river has a current of 5mph. It takes Al half an hour longer to paddle upstream
1.2 miles than to paddle downstream the same distance.
What is Al's rate in still water.
:
Let s = his paddling rate in still water
then
(s+5) = his effective speed downstream
and
(s-5) = his effective speed upstream
:
Write a time equation, time = dist/speed
:
upstream time = downstream time + .5 hrs
=
:
multiply by (s-5)(s+5) to clear the denominators, results:
1.2(s+5) = 1.2(s-5) + .5(s+5)(s-5)
1.2s + 6 = 1.2s - 6 + .5(s^2 - 25)
:
Combine on the right
0 = 1.2s - 1.2s - 6 - 6 + .5s^2 - 12.5
:
Combine like terms, arrange as a quadratic equation
.5s^2 - 24.5 = 0
:
multiply by 2 to clear the decimals
s^2 - 49 = 0
s^2 = +49
s =
s = 7 mph in still water
:
:
See if this is true, find the times
1.2/(7-5) = .6 hrs upstream
1.2/(7+5) = .1 hrs down
-------------------
time dif: = .5 hrs
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