Question

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

Answer 1

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