Car A starts in Sacramento at 11am It travels along 400 mile

Car A starts in Sacramento at 11am. It travels along 400 mile route to LA at 50mph. Car B starts from Los Angeles at noon and travels to Sacramento along the same route at 75 mph. The route goes past Fresno which is 150 miles along the route from Los Angeles. How far from Fresno are the cars when they meet?

Solution

Let the cars meet at a time t after 12 noon.
The speed of car A = 50 mph
The distance travelled by A in(t+1)hours is x = 50(t+1)miles
The speed of car B = 75 mph
The distance travelled by B in t hours is y = 75t miles
But, x+y = 400 miles
50(t+1)+75t = 400
50t+50+75t = 400
125t = 400-50
125t = 350
t = 350/125
t = 2 100/125 hours
t = 2h 48 minutes
The distance travelled by B = 75t = 210 miles
But Fresno is 150 miles from LA
So the distance between the point of meeting and Fresno = 210-150 = 60 miles