Martina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Martina drove home, there was no traff

Question

Martina drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took
6
hours. When Martina drove home, there was no traffic and the trip only took
4
hours. If her average rate was
22
miles per hour faster on the trip home, how far away does Martina live from the mountains?
Do not do any rounding.

Answer 1

d = r · t

 

for the trip going

d = r · 6

 

for the trip returning

d = (r + 22) · 4

 

6r = 4(r + 22)

6r = 4r + 88

2r = 88

r = 44

 

d = 44 · 6

d = 264

Answer 2

Let's imagine that going to the mountains she traveled at x miles per hour.  Then according to the problem, on the way home, without traffic, she traveled at x + 22 miles per hour.

We know that the distance is the same in each direction. 

If she traveled at speed x for 6 hours going to the mountains, the distance she traveled was 6x.

Coming home she traveled at speed (x + 22) for 4 hours, or 4(x + 22).

But since the distance is the same each way, we can say

6x = 4(x + 22)

Now we can just manipulate the equation to solve for x.

6x = 4x + 88

2x = 88

x = 44.

If x = 44, then her trip to the mountains we 6 hours times 44 miles per hour, or 264 miles.