SOLUTION: Bryce ran a 4 mile race at a constant speed of 10 mph. Conner left at the same time and started out fast for the first mile. During this time, his speed did not vary. At the end

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Question 566577: Bryce ran a 4 mile race at a constant speed of 10 mph. Conner left at the same time and started out fast for the first mile. During this time, his speed did not vary. At the end of the first mile he blew up and had to go 6 mph slower the last 3 miles. Both crossed the finish line at the same time. How fast did Conner run the first mile? Show all of your work.
Answer by lwsshak3(11628) About Me  (Show Source):
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Bryce ran a 4 mile race at a constant speed of 10 mph. Conner left at the same time and started out fast for the first mile. During this time, his speed did not vary. At the end of the first mile he blew up and had to go 6 mph slower the last 3 miles. Both crossed the finish line at the same time. How fast did Conner run the first mile? Show all of your work.
**
x=Conner's speed for the first mile
x-6=Conner's speed for the remaining 3 miles
Travel time=distance/speed (same for both runners)
..
4/10=1/x+3/(x-6)
LCD:10x(x-6)
4x(x-6)=10(x-6)+3(10x)
4x^2-24x=10x-60+30x
4x^2-64x+60=0
x^2-16x+15=0
(x-15)(x-1)=0
x=1 (reject, not reasonable)
or
x=15
ans:
Conner's speed for the first mile=15 mph