A train traveling at 50 miles per hour leaves for a certain

A train traveling at 50 miles per hour leaves for a certain town. Two hours
later, a bus (starting at the same point as the train) traveling at 60 miles
per hour leaves for the same town and arrives at the same time as the train.
If both the train and the bus traveled in a straight line, how far is the town
from where they started?

Solution

Make this chart

DISTANCE RATE TIME
TRAIN
BUS   

Let x be the required distance from where they started
to the town. They both traveled the same distance,
so put x for both distances

DISTANCE RATE TIME
TRAIN x   
BUS x

Put in their rates which are given:

DISTANCE RATE TIME
TRAIN x 50   
BUS x 60   

Now fill in the TIMES by using TIME=%28DISTANCE%29%2F%28RATE%29

DISTANCE RATE TIME
TRAIN x 50 x/50
BUS x 60 x/60

The train\'s time was two hours more than the bus\'s time,
so

TRAIN\'S TIME = BUS\'S TIME + 2 HOURS

x/50 = x/60 + 2

x%2F50=x%2F60%2B2

Multiply through by 300

6x+=+5x%2B600

x=600

So the town is 600 miles from where they started.