SOLUTION: you take 94 minutes to complete a 10-mi race. your average speed during the first five miles of the race is 2 mph faster than your average speed during the second five miles of the

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Question 868642: you take 94 minutes to complete a 10-mi race. your average speed during the first five miles of the race is 2 mph faster than your average speed during the second five miles of the race. what is your average speed during the first half of the race? how long to the nearest minute did it take you to run the first five miles?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= speed in mph during the second five miles of the race.
x%2B2= speed in mph during the first five miles of the race.
5%2Fx= hours running for the second five miles of the race.
60%2A%285%2Fx%29=300%2Fx= minutes running for the second five miles of the race.
5%2F%28x%2B2%29= hours running for the first five miles of the race.
60%2A%285%2F%28x%2B2%29%29=300%2F%28x%2B2%29= minutes running for the first five miles of the race.
300%2F%28x%2B2%29%2B300%2Fx=94 is the total time running, in minutes.Multiplying both sides of the equal sign time %28x%2B2%29x we get
300x%2B300%28x%2B2%29=94%28x%2B2%29x
300x%2B300x%2B600=94%28x%5E2%2B2x%29
600x%2B600=94x%5E2%2B188x
0=94x%5E2%2B188x-600x-600
94x%5E2-412x-600=0
x+=+%28412+%2B-+sqrt%28412%5E2-4%2A94%2A%28-600%29%29%29%2F%282%2A94%29+
x+=+%28412+%2B-+sqrt%28169744%2B225600%29%29%2F188+
x+=+%28412+%2B-+sqrt%28395344%29%29%2F188+
Rounding that square root to 628.76 we get
x=%28412+%2B-+628.76%29%2F188
Since we are looking for a positive x value,
x=%28412+%2B+628.76%29%2F188=1040.76%2F188=5.536
So the average speed (in mph) during the second five miles of the race was x=5.536 ,
and the average speed (in mph) during the first five miles of the race was
x%2B2=highlight%287.536%29
At that speed, the first 5 miles took
5%2F7.536 hours = 5%2A60%2F7.536 minutes = about highlight%2840%29 minutes (rounded to the nearest minute).