A car travels 180mi a second car traveling 15mih faster than

A car travels 180mi, a second car, traveling 15mi/h faster than the first car , makes the trip in 1 hr less time. Find the speed of each car.

Solution

1st car DATA:
distance = 180 miles ; rate = x mph ; time = d/r = 180/x hrs
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2nd car DATA:
distance = 180 miles ; rate = \"x+15\" mph ; time = d/r = 180/(x+15)
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EQUATION:
1st car time - 2nd car time = 1 hr.
180/x - 180/(x+15) = 1
180x + 180*15 - 180x = x^2+15x
x^2 + 15x -15*180 = 0
x = [-15 +- sqrt(15^2-4*-15*180)]/2
x = [-15 +- 105]/2
Positive solution:
x = 45 (rate of the 1st car)
x+15 = 60 (rate of the 2nd car)