A car travels 60 miles in the same time that a car traveling

A car travels 60 miles in the same time that a car traveling 10 per hour faster travels 90 miles. What is the rate of each cars?

Solution

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r

Let r=rate of slower car
Then r+10=rate of faster car
Time for slower car to travel 60 mi=(d/r)=60/r
Time for faster car to travel 90 mi=(d/r)=90/(r+10)
And we are told that the above two times are equal, so:
60/r=90/(r+10) multiply each side by r(r+10) or just cross-multiply
60(r+10)=90r get rid of parens
60r+600=90r subtract 60r from both sides
60r-60r+600=90r-60r collect like terms
600=30r divide both sides by 30
r=20 mph-------------------------speed of slower car
r+10=20+10=30 mph ---------------------speed of faster car
CK
60/20=90/30
3=3