Pleasee help.. I tried 5 timess !!!!! MATH WORD PROBLEM

Question

Elsa drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
7 hours. When Elsa drove home, there was no traffic and the trip only took 4 hours. If her average rate was
27 miles per hour faster on the trip home, how far away does Elsa live from the mountains?

Answer 1

Speed= Distance/Time

 

For the trip going,

Let X=speed going

Let D= distance between her home and the mountain

and we know the time of the trip is 7 hours.

 

For the trip returning,

Let X+27= speed returning

Let D= distance between her home and the mountain

and we know the time of the trip is 4 hours.

 

So we have discovered the following 2 equations:

X=D/7 (this equation is for the trip going)

X+27=D/4 (this equation is for the trip returning)

 

Since X=D/7, then D=7X.

Now we plug this into the equation for the returning trip:

X+27= 7X/4

4(X+27)= 4(7X/4)

4X+108= 7X

108= 3X

X=36

 

We have found out X=36, now we can plug X back into the first equation:

X=D/7

36=D/7

36*7=D

D=252

 

So we know distance between her home and the mountain is 252 miles.

 

 

 

 

 

 

Answer 2

distance=rate*time

d=rt

d=r*7              going to the mountains

d=(r+27)*4     returning from the mountains     

they are both equal to d so set them equal to each other

 

7r=4(r+27)

7r=4r+108

7r-4r=108

3r=108

r=108/3

r=36 mph

d=rt

d=36*7

d=252 miles, or...

d=(36+27)*4

d=63*4

d=252 miles