A bus traveling at an average rate of 30 miles per hour left

A bus traveling at an average rate of 30 miles per hour left the city at 10:00 am. A car left 2 hours later, following the bus at 45 miles per hour. How many hours until they are both the same distance from the city?

Solution

d=rt
d=30t for the bus.
d=45(t-2) for the car.
Set the distances equal.
30t=45(t-2)
30t=45t-90
30t-45t=-90
-15t=-90
t=-90/-15
t=6 hours after the bus leaves they will be the same distance from the city.
Proof:
30*6=45(6-2)
180=45*4
180=180 miles from the city after 6 hours.