Question

Anne drove to her friend's house at a speed of 55 mph. On the way home she could only drive 35 mph. It took her 2 hours longer on the way back. How many miles is it to her friends home?

Answer 1

192.5 miles

Explanation:

let h be number of hours Anne takes to drive to her friend's house

`(55mph)(h) = (35mph)(h+2)`

Both sides of this equation represent the miles to her friend's home. (speed * time = distance)

We add 2 to h on the right side because the way back takes 2 hours longer than the way to her friend's home.

Now we can solve.

`(55)(h) = (35)(h+2)\\55h = 35h+70\\20h = 70\\h = (7)/(2) = 3.5`

Now that we have how long the trip to her friend's house takes, we can solve for the distance to her friend's house by using either side of our equation. I will use the left side because it is simpler.

`(55)(h)\\(55)(3.5)\\\boxed{192.5}`

That is the answer

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