Question

Emile is a long-distance runner. He runs at a constant speed of six miles/hour. His goal is to run nine miles on each practice run, but he normally runs a distance that varies three miles more or less than that. Select the correct answer from each drop-down menu. The equation that can be used to find the minimum and maximum time (in hours) Emile runs is_____. For each practice run, the minimum number of hours Emile runs is______ and the maximum number of hours he runs is ______.

Answer 1

`t=(9\pm 3)/(6)`

`1\ \text{hour}`

`2\ \text{hour}`

Explanation:

s = Speed of Emile = 6 miles/hour

d = Distance traveled by Emile =
`(9\pm 3)\ \text{miles}`

Time taken to find the minimum and maximum time Emile ran for is

`t=(d)/(s)\\\Rightarrow t=(9\pm 3)/(6)`

The required equation is
`t=(9\pm 3)/(6)`

The time taken is

`t=(9-3)/(6)\\\Rightarrow t=(6)/(6)\\\Rightarrow t=1\ \text{hour}`

The minimum number of hours Emile runs is 1 hour.

`t=(9+3)/(6)\\\Rightarrow t=(12)/(6)\\\Rightarrow t=2\ \text{hour}`

The maximum number of hours Emile runs is
`2\ \text{hour}`.

Answer 2

|6x – 9| = 3

1 Hour

2 Hours

Explanation:

The equation that can be used to find the minimum and maximum time (in hours) Emile runs is_|6x – 9|= 3_. For each practice run, the minimum number of hours Emile runs is__1 hour_ and the maximum number of hours he runs is _2 hour.