SOLUTION: You drive from Phoenix to Santa Fe, a distance of 480 miles. A week later you return using the same route. On the way back to Phoenix your average speed is 5 miles per hour faster

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Question 1049036: You drive from Phoenix to Santa Fe, a distance of 480 miles. A week later you return using the same route. On the way back to Phoenix your average speed is 5 miles per hour faster. This made a 25-minute difference in time. Find the average speed for the trip there and the average speed for the trip back. Find the total time it took to drive there and the total time it took to drive back.
Answer by jorel555(1290) About Me  (Show Source):
You can put this solution on YOUR website!
Let r represent your speed in mph. 25/60=5/12 hour. So:
480/r=480/(r+5)+5/12 hr
5760/r=5760/(r+5)+5
5760(r+5)=5760r+5(rē+5r)
5760r+28800=5760r+25r+5rē
5rē+25r-28800=0
rē+5r-5760=0
Using the quadratic formula; we get r=73.436, and -78.436. Throwing out the negative result, we get the average speed going there as 73.436 mph; going back the average speed was 78.436.
Total drive time there:480/73.436=6.54 hours
Total drive time back:480/78.436=6.12 hours