Two trains start heading toward each other from two cities, the distance between which is 720 km and meet right in the middle. The second train left 1 hour after the first train, but traveled at a speed 4 km/hour faster than the first train. Find the speed of both trains.

Two trains start heading toward each other from two cities, the distance between which is 720 km, and meet right in the middle.

The second train left 1 hour after the first train, but traveled at a speed 4 km/hour faster than the first train.

Find the speed of both trains.

:

If they met half-way, each train traveled 360 mi

let s = speed of the slower train

then

(s+4) = speed of the faster train

:

Write a time equation

Slow train time - fast train time = 1 hr

- = 1

multiply equation by s (s+4), cancel the denominators 360 (s+4) - 360s = s (s+4) 360s + 1440 - 360s = s^2 + 4s

A quadratic equation

0 = s^2 + 4s - 1440

Use the quadratic formula; a=1; b=4; c=-1440. but this will factor to:

(s-36) (s+40) = 0

positive solution

s = 36 mph, speed of the slow train

then obviously;

40 mph, the speed of the faster

:

:

Check this by finding the actual time of each

360/36 = 10 hrs

360/40 = 9 hrs, 1 hr less