Bunuel wrote:

Toledo and Cincinnati are 200 miles apart. A car leaves Toledo traveling toward Cincinnati, and another car leaves Cincinnati at the same time, traveling toward Toledo. The car leaving Toledo averages 15 miles per hour faster than the other, and they meet after 1 hour and 36 minutes. What is the speed of the faster car in miles per hour?

A. 55

B. 66

C. 70

D. 81

E. 110

"Closing the gap" approachWe need the speed of the faster car, "Car A." Slower car = "Car B"

Distance between Car A and Car B = 200 miles = gap distance

Time taken to close the distance gap: 1 hour 36 minutes

\(=1\frac{36}{60}hrs=1\frac{3}{5}hrs=\frac{8}{5}\) hours

Speeds/rates*. Car A travels 15 miles per hour faster than Car B

Let \(r\) = speed of faster Car A

So \((r-15)\) = speed of slower Car B

Relative / Combined speedCars travel in opposite directions, so ADD speeds to find the relative speed at which the distance gap is closed

Relative speed: \((A_{r}+B_{r})=r+ (r-15)\)

Solve with the standard RT=D formula

\(r_{relative}*t=D\)

\((r+r-15)*\frac{8}{3}=200\)

\((2r-15)(8)=1,000\)

\((16r-120)=1,000\)

\(16r=1,120\)

\(r=70\)

Faster Car A travels at 70 mph

Answer C

* Or use \(r\) = slower car and \(r+15\) = faster car. In that case, we are solving for the rate of the slower car, which is trap answer A. We need to add 15 to the rate of the slower car to get the correct answer.
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