The sum of the speeds of two trains is 721.5 miles per hour. If the speed of the first train is 8.5 mph faster than that of the second train, find the speeds of each.

365.0 mi/h; 356.5 mi/h

Step-by-step explanation:

Let x = speed of first train

and y = speed of second train

We have two conditions:

(1) x + y = 721.5

(2) x = y + 8.5

Subtract y from each side of (2) (3) x - y = 8.5

Add (1) and (3) 2x = 730.0

Divide each side by 2 (4) x = 365.0

Substitute (4) into (1) 365.0 + y = 721.5

Subtract 365.0 from each side y = 356.5

The first train travels at 365.0 mi/h, and the second train travels

at 356.5 mi/h.

Check:

365.0 + 356.5 = 721.5 365.0 = 356.5 + 8.5

721.5 = 721.5 365.0 = 365.0