Question

Yesterday, Carmen went on a bike ride. Her average speed was 8

miles per hour. Today, she went on another ride, this time averaging 13
miles per hour. In the two days, she biked for a combined total time of 9
hours.
Let x
be the number of hours she biked yesterday. Write an expression for the combined total number of miles she biked in the two days.

Answer 1

Explanation:

Yesterday, her rate was 8mph, her time was x hours.

Today, her rate was 13mph, her time was 13 - x hours.

So the total distance she biked on the two days is

d = 8x + 13(13 - x), or 169 - 5x

Answer 2

`8x+13(9-x)` or
`-5x+117` miles.

Explanation:

Let x represent number of hours Carmen biked yesterday.

`\text{Distance}=\text{Speed}* \text{Time}`

We have been given that yesterday Carmen's average speed was 8

miles per hour. So distance covered in x hours would be
`8x`.

We are also told that Carmen biked for a combined total time of 9

hours. So the number of hours biked second day would be
`9-x`. The distance covered in
`9-x` at a speed of 13 miles per hour would be
`13(9-x)`.

Total distance covered by Carmen would be:
`8x+13(9-x)`

`8x+117-13x`

`8x-13x+117`

`-5x+117`

Therefore, the total distance covered by Carmen in the two days would be
`-5x+117` miles.