<PRE><B>Question 309433</B>
 You drive to California. On the way, you averaged 10 miles per hour less, and the drive took you 5 extra hours. What was your average speed on thw\e way to California?
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I would do it this way:
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Let r = speed on the way to Calif
then
(r+10) = speed on the return trip
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Let 1500 mi = one way distance
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Write a time equation; time = dist/speed
to Calif time - return time = 5 hrs
{{{1500/r}}} - {{{1500/(r+10)}}} = 5 hrs
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multiply by r(r+10), results:
1500(r+10) - 1500r = 5r(r+10)
1500r + 15000 - 1500r = 5r^2 + 50r
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Combine on the right
0 = 5r^2 + 50r - 15000
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simplify, divide by 5, results
r^2 + 10r - 3000 = 0
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Factors to
(r+60)(r-50) = 0
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the positive solution is what we want here
r = 50 mph is the speed to Calif
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Check solutions by finding the times: (return trip speed = 60 mph)
1500/50 = 30 hrs
1500/60 = 25 hrs
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time dif: 5 hrs


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