Question

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.

Answer 1

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 denominators360(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