SOLUTION: You commute to work a distance of 80 miles and return on the same route at the end of the day. Your average rate on the return trip is 10 miles per hour faster than your average r
Algebra.Com
Question 148238: You commute to work a distance of 80 miles and return on the same route at the end of the day. Your average rate on the return trip is 10 miles per hour faster than your average rate on the outgoing trip. If the round trip takes 3 hours, what is your average rate on the outgoing trip to work?
Let x be the rate for the outgoing trip.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
You commute to work a distance of 80 miles and return on the same route at the end of the day. Your average rate on the return trip is 10 miles per hour faster than your average rate on the outgoing trip. If the round trip takes 3 hours, what is your average rate on the outgoing trip to work?
:
Let x = the rate for the outgoing trip.
then
(x+10) = rate for the return trip
:
Write a time equation: Time =
:
Out time + return time = 3 hrs
+ = 3
Multiply equation by x(x+10) the common denominator
80(x+10) + 80x = 3x(x+10)
:
80x + 800 + 80x = 3x^2 + 30x
:
160x + 800 = 3x^2 + 30x
:
arrange as quadratic equation:
3x^2 + 30x - 160x - 800 = 0
:
3x^2 - 130x - 800 = 0
:
We need to solve this using the quadratic formula:
In this equation a=3; b=-130; c= -800
:
:
:
:
We're only interested in the positive solution here
x =
x = 48.8 mph is the outgoing rate.
then
48.8 + 10 = 58.8 is the return rate
:
:
Check solution by finding the total time
80/48.8 + 80/58.8 =
1.64 + 1.36 = 3.00 hrs
RELATED QUESTIONS
You commute to work a distance of 40 miles and return on the same route at the end of the (answered by Fombitz)
You commute to work at a distance of 40 miles and return on the same route at the end of... (answered by ikleyn)
1) A Commuter bus takes 2 hours to get downtown: an express bus, averaging 25mph faster,... (answered by Paul)
A man commutes to work a distance 35 miles and returns on the same route at the end of... (answered by ankor@dixie-net.com)
The average rate of a round trip having a one way distance of d is given by the complex... (answered by ankor@dixie-net.com)
a man commutes to work a distance of 30 miles and teturns on the same route at the end of (answered by ankor@dixie-net.com)
You ride your bike to campus a distance of 5 miles and return home on the same route.... (answered by ankor@dixie-net.com)
Mr. Newton drive to and from work over the same route each day. On Friday, he drives at... (answered by ankor@dixie-net.com)
You drive from Phoenix to Santa Fe, a distance of 480 miles. A week later you return... (answered by jorel555)