I drive to the mountains and it takes 6 hours. I drive home and it takes 4 hours. If I averaged 22 MPH faster coming home how far do I live from the mountains

Answer 1

We will use the distance = rate x time formula.

Based on the question, you drove straight to the mountain and straight back, so the distance traveled will be the same for the trip there and the trip back.

Lets figure the “to” trip:

6R=R x 6

Now let’s figure the “return” trip:

4(R+22)=R+22 x 4

Since the distances are equal, this is what we have now:

6R=4(R+22)

6R=4R+88

-4R -4R

2R=88

/2 /2

R=44

Now put the rate of 44 into the first equation so we can solve for distance.

D=44 x 6

D=264

Answer 2

The distance to the mountains is the same both ways.

Let x = average speed going to the mountains

y = average speed coming back from the mountains

So, 6x will be the distance to the mountains and 4y will be the distance coming back which is the same. Therefore, 6x = 4y. We also know that the average speed coming back from the mountains, y, is 22mph faster than going there---> y = x + 22.

Thus, we have: 6x = 4y

6x = 4(x + 22)

6x = 4x + 88

2x = 88

x = 44 average speed going to the mountains

The distance to the mountains is 6x, or 6(44) = 264 miles. You will find that this is the same coming home.

Hope this helps!