Solving a Word Problem

Question

Outside a city, a highway and railroad track run parallel to each other for many miles. If a car starts down the highway at 55 miles per hour and a train leaves the city 45 minutes later going 70 miles per hour in the same direction, how long will the train take to catch up with the car?

Answer 1

distance=rate*time

d=r*t

d=55*t

d=70*(t-0.75)  because 45 min=45/60=3/4=0.75 hours

equate the two right sides

55t=70(t-0.75)

55t=70t-52.5

55t-70t=-52.5

-15t=-52.5

15t=52.5

t=52.5/15

t=3.5 hours

3.5-0.75=2.75 hours until the train catches up with the car

Answer 2

The distance for the train from the city (point A) to the catch up point (point C) is s miles

train leaves after 45 min = 0.75 hr

In 0.7 hr the car traveled (55) (0.75)= 41.25 mile where the car reaches a point B.

The time needed for the car to travel the distance (s-41.25) mile is the same time for the train to cover the distance s mile.

 Let we call this time just t.

Therefore

 

t = (s-41.25)/55 for the car and same time

t = s/70  for the train

t=t or

(s-41.25)/55 = s/70,  s = 192.5 mile the distance from A to C

For the train to travel a distance 192.5 with a velocity of 70 mph means the time will be

t=192.5/70 = 2.75 hr

For the car the distance will be 192.5 - 41.25 = 151.25 mile.  The elapsed time for the car for this distance from B to C:

t = 151.25/55 = 2.75 hr.