The green river freeway has a minimum and maximum speed limit, tony drove for 2 hours at the minimum speed limit and 3.5 hours at the maximum speed, a distance of 355 miles. Rae drove 2 hours at the minimum speed limit and 3 hours at the maximum speed limit, and distance of 320 miles. What are the two speeds? Write and solve tony and Rae's distances

From the beginning we know we are dealing with two different rates. Distance is equal to (Speed X Time). We have two different speeds though. We will call the min speed = x and the max speed = y. With those two ideas in place we can make two equations for both Tony and Rae.

Tony:

2x+3.5y=355

Rae:

2x+3y=320

Now you can solve the equations by subtracting Rae's equation from Tony's

.5y=35 solve for y and you get 70

Now plug that y value back into either equation and you can solve for x. I'll use Rae's distance:

2x+3 (70) = 320

x=55