a passenger train leaves a train depot 2.5 after a freight train leaves the same depot the passenger train is traveling 13 mph faster than the freight train. find the rate of each train if the passenger train overtakes the freight in 5 h

Freight = 13 mph

Passenger = 26 mph

Step-by-step explanation:

Givens

Freight Train

Rate = r

time = 5 hours

distance = 5*r

Passenger Train

r = r + 13

t = 2.5 hours

d = (r + 13) * 2.5

Formula

The distances are the same so the rate times the time can be equated.

(r + 13) * 2.5 = 5*r

Solution

Divide both sides by 2.5

(r + 13) * 2.5 / 2.5 = 5 * r / 2.5

r + 13 = 2r Subtract r from both sides.

r - r + 13 = 2r - r

13 = r Switch and divide by 1.5

r = 13 Freight train

r + 13 = 13 + 13 = 26 mph. Passenger train.

Both trains traveled a distance of 65 miles. See if you can see why.