SOLUTION: Thank you in advance if you are able to help solve the word problem for me. The question is, "Your commute to De Anza from San Francisco is 40 miles and your average rate of your r

Question 718562: Thank you in advance if you are able to help solve the word problem for me. The question is, "Your commute to De Anza from San Francisco is 40 miles and your average rate of your return trip is 30 miles per hour faster than your average rate of going to De Anza. If the round trip takes 2 hours, what is your average rate coming to school?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Your commute to De Anza from San Francisco is 40 miles, and your average rate of your return trip is 30 miles per hour faster, than your average rate of going to De Anza.
If the round trip takes 2 hours, what is your average rate coming to school?
:
let s = your speed to Anza
then
(s+30) = return trip speed
:
Write a time equation; time = dist/speed
:
To time + return time = 2 hrs
+ = 2
multiply equation by s(s+30), resulting in:
40(s+30) + 40s = 2s(s+30)
40s + 1200 + 40s = 2s^2 + 60s
arrange as a quadratic equation on the right
0 = 2s^2 + 60s - 80s - 1200
2s^2 - 20s - 1200 = 0
Simplify, divide by 2
s^2 - 10s - 600 = 0
Factors to
(s+20)(s-30) = 0
the positive solution is all we want here
s = 30 mph to Anza
and
30 + 30 = 60 mph return
:
:
See if that checks out, find the actual time each way
40/30 = 1.33 hrs
40/60 = .67 hrs
---------------
total time: 2 hrs
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