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

Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let t=time it takes bus and train to arrive at the town after bus starts
Distance train travels=50*2+50t (Note: train already has a 2 hour head start)
Distance bus travels=60t
When the above two distances are equal they will have arrived at the town, so:
100+50t=60t subtract 50t from each side
100+50t-50t=60t-50t collect like terms
100=10t divide each side by 10
t=10 hours-------------------------time it takes the bus and train to arrive after bus starts
d=rt; d=60*10=600 mi--------distance to town
CK
100+50*10=60*10
100+500=600
600=600