SOLUTION: Simone and Sean are running in a four-mile relay race. After Simone completes the first two miles, Sean runs the second two miles. Sean runs 1 mile per hour slower than Simone. Tog

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Simone and Sean are running in a four-mile relay race. After Simone completes the first two miles, Sean runs the second two miles. Sean runs 1 mile per hour slower than Simone. Tog      Log On

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Question 973854: Simone and Sean are running in a four-mile relay race. After Simone completes the first two miles, Sean runs the second two miles. Sean runs 1 mile per hour slower than Simone. Together they complete the race in 0.9 hours. How fast did each person run? Justify your answer.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Simone and Sean are running in a four-mile relay race. After Simone completes the first two miles, Sean runs the second two miles. Sean runs 1 mile per hour slower than Simone. Together they complete the race in 0.9 hours. How fast did each person run?
***
let x= Sean's speed
x+1=simon's v speed
travel time=distance / speed
2%2Fx%2B2%2F%28x%2B1%29=0.9
lcd: x(x+1)
2(x+1)+2x=0.9(x^2+x)
mult. by 10
20(x+1)+20x=9(x^2+x)
20x+20+20x=9x^2+9x
9x^2-31x-20=0
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=9, b=-31, c=-20
x+=+%2831+%2B-+sqrt%28+31%5E2-4%2A9%2A-20%29%29%2F%282%2A9%29+
x+=+%2831+%2B-+sqrt%28+961%2B720%29%29%2F%2818%29+
x+=+%2831+%2B-+sqrt%281681%29%29%2F%2818%29+
x+=+%2831+%2B-+sqrt%281681%29%29%2F%2818%29+
x+=+%2831+%2B41%29%2F%2818%29=72%2F18=4+
How fast did each person run?
Sean: 4 mph
Simon: 5 mph