<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 the way to California? 
This is the formula I used but not sure how to solve it:
1500=(R-10)(T+5)
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From-California DATA:
distance = 1500 miles ; rate = r mph ; time = t hrs
Note: rt = 1500
t = 1500/r 
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To-California DATA:
distance = 1500 miles ; rate = r-10 mph ; time = t+5 hrs
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Note: (r-10)(t+5) = 1500 
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You have two equations; solve the system:
rt-10t+5r-50 = 1500
1500 -10(1500/r)+5r-50 = 1500
-10(1500/r)+5r-50 = 0
Multiply thru by r to get:
-10(1500) + 5r^2 - 50r = 0
Divide thru by 5 to get:
-2(1500) + r^2 - 10r = 0
r^2 -10r - 3000 = 0
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r = [10 +- sqrt(100+4*3000)]/2
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r = [10 +- sqrt(12100)]/2
Positive solution:
r = [120]/2
r = 60 mph
t = 1500/60 = 25 hrs.
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Cheers,
Stan H.
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