Linear Equation Word Problem

Question

Margaret drove to a business appointment at 50 MPH. Her average speed on the return trip was 40 MPH. The return trip took her 1/4 hour longer because of heavy traffic. How far did she travel to the appointment?

Answer 1

If distance = rate x time, let's set up two equations, one for her trip to her appointment and one for her trip home.  In each case the distance would be the same.

 

Using d = rt

r_g = her rate going to her appointment = 50 mph

r_h = her rate going home = 40 mph

t_g = time it took to get to the apointment

t_h = time it took to get home

We are told that t_h = t_g + .25

 

d = 50t_g

and

d = 40t_h = 40(t_g + .25)

 

Since both equations are the distance from home to the appointment, we can set them equal to one another.

50t_g = 40(t_g + .25)

50t_g = 40t_g + 10

10t_g = 10

t_g = 1 hour

 

Knowing one of the times, we can determine the distance

d = r_g t_g

d = 50 (1)

d = 50 miles