Kathy and Brian drove a total of 750 miles in 12 hours. Kathy drove the first part of the trip at 65 miles per hour and Brian drove the remaining part of the trip at 55 miles per hour.

Question

This is what you should solve: For what length of time did Kathy and Brian drive?

Answer 1

rate * time = distance.

Let x = number of hours Kathy drove.

Let y = number of hours Brian drove.

The total distance traveled is the distance Kathy drove plus the distance Brian drove. But we don't know how far they drove, and we don't have a variable for it. But we do have a variable for how many hours each one drove, and we have the formula rate * time = distance.

750 = distance Kathy drove + distance Brian drove.

750 = 65 x + 55 y

We know that between the two of them, they drove for 12 hours.

12 = x + y

You have two equations and two unknowns. multiply the second equation by -55 to get

-660 = -55 x - 55 y

Then add the first equation to this one to get:

90 = 10 x

So Kathy drove for 9 hours and Brian drove for the remaining 3 hours.