How far did she travel to the appointment?

Question

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

Answer 1

Hi E.b. P.,

In this problem we are given speed, a partial time, and asked for distance. For an object distance over time is speed, d/t = s, or distance equals speed times time, d = s*t.

Lets write an equation for the distance to the business and call it d_tb (tb for to business):

d_tb = 50*t; (speed is 50 mph)

Lets write an equation for the return trip from the business and call it d_rt (rt for return trip):

d_rt = 40*(t + 1/4); (speed is 40 mph and return trip time is 1/4 hr longer than trip time to business)

And the distance to the business is equal to the distance of the return trip:

d_tb = d_rt;

50*t = 40*(t + 1/4); (plug in values for d_tb and d_rt)

50*t = 40*t + 10

10*t = 10

t = 1

This question asks for the distance to the business, d_tb:

d_tb = s*t;

d_tb = 50*1;

d_tb = 50 miles; (we have miles per hour, mph, with miles as our distance)

I hope this helps, Joe.