SOLUTION: I hope you can help A car travels 180 miles. A second car, traveling 15 m/h faster than the first car, makes the same trip in 1 hour less time. Find the speed of each car.

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Question 244059: I hope you can help
A car travels 180 miles. A second car, traveling 15 m/h faster than the first car, makes the same trip in 1 hour less time. Find the speed of each car.
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the distance traveled by the first car.

Let represent the speed of the first car

Let represent the travel time of the first car

Then represents the distance traveled by the second car also.

And represents the speed of the second car

And represents the travel time for the second car.

Since we know that distance is equal to rate times time, we can say with respect to the trip taken by the first car:

And with respect to the trip taken by the second car:

Multiply the second equation by

Add 1 to both sides:

Multiply the first equation by

Set the two expressions that are equal to Let equal to each other:

Simplify and then solve the resulting quadratic for . Exclude the negative root. The positive root will be the speed of the first car. Add 15 to find the speed of the second car.

John