Please help answer with steps thanks so much.

Question

Angela drove at an average speed of 55 mi/h from her home in Memphis to visit her sister in Miami. She stayed in Miami 25 hours, and on the trip back averaged 40 mi/h. She returned home 49 hours after leaving. How many miles is Memphis from Miami?

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

Answer 1

First, figure out how much time she was traveling.

 

If she returned home 49 hours after leaving and spent 25 hours in Miami, she was traveling:

 

49 - 25 = 24 hours

 

So, if t is the time from Memphis to Miami, the time from Miami to Memphis is 24 - t

 

Use the equation d = rt 

 

d = distance

r = speed

t = time

 

On the trip from Memphis to Miami:

 

d = (55 mph)(t)

 

On the trip from Miami to Memphis:

 

d = (40 mph)(24 - t)

 

You know that the distance going to Miami is the same as the distance returning from Miami, so:

 

(55)(t) = (40)(24 - t)

 

Now solve for t

 

55t = 960 - 40t

95t = 960

t = 10.1 hours

 

Now use this number to find the distance. You can use either of the two distance equations above. I'll use the first one:

 

d = (55)(t) = (55)(10.1) = 556 miles

 

To check, plug t into the second distance equation:

 

d = (40)(24 - t) = (40)(24 - 10.1) = 556 miles

 

It checks!

 

Let me know if you have any questions.