Melissa drove at an average speed of 45 mi/h from her home in Memphis to visit her sister

Question

Melissa drove at an average speed of 45 mi/h from her home in Memphis to visit her sister in Atlanta. She stayed in Atlanta 10 hours, and on the trip back averaged 60 mi/h. She returned home 43 hours after leaving. How many miles is Memphis from Atlanta?

a) Write an equation using the information as it is given above that can be solved to answer this question. Use t as your varible to represent the amount of time Melissa spent driving from Memphis to Atlanta.
Equation:

b) How many miles is Memphis from Atlanta?
Answer: miles

Give your answer to the nearest mile

Answer 1

First, subtract the 10 hours Melissa wasn't driving.  She drove for a total of 33 hours.

Speed = distance/time, so time = distance/speed.

Memphis to Atlanta:  t = d/45.

Atlanta to Memphis:  33 - t = d/60.

So d/45 + d/60 = 33.

LCD = 180, so 4d/180 + 3d/180 = 5940/180.

All denominators are equal, so 4d + 3d = 5940.  4d + 3d = 7d, so 7d = 5940.

d = 5940/7 = 848.57 = 849.  This is the one-way distance between Memphis and Atlanta.

CHECK:  It took Melissa 848.57/45 = 18.86 hours to drive from Memphia to Atlanta and 848.57/60 = 14.14 hours to drive back to Memphis.  18.86 + 14.14 = 33.