Question

Sam ran 63,756 feet in 70 minutes. What is Sam's rate in miles per hour?

Answer 1

Sam's rate is `(10.35 "miles")/(hour")`

Explanation:

Let's break the answer down into three parts:

`color (magenta) ("First,"` we're going to convert feet to miles using this conversion factor:
`color(white)(aaaaaaaaaaaaaaaaa` 1 mile = 5,280 feet

`color (blue) ("Then,"` we're going to convert minutes to hours using the relationship below:
`color(white)(aaaaaaaaaaaaaaaaa` 1 hour = 60 minutes

`color (red) ("Finally,"` we are going to divide the value that we get in miles by the value that we get in hours, since the word "per" means to divide.

`color (magenta) ("Step 1:"`

`63,756 cancel"feet"xx("1mile"/("5,280"cancel"feet"))` = `12.075 "miles"`

`color (blue) ("Step 2:"`

`70 cancel"minutes"xx((1"hour")/(60cancel"minutes"))` `= 1.1667 "hours"`

`color (red) ("Step 3:"`

`(12.075 "miles")/(1.167 "hours")` `= (10.35 "miles")/(hour")`

Answer 2

Sam's speed is about 10.3 mi/h.

Explanation:

Use dimensional analysis.

Determine the equality between miles and feet, and hours and minutes.

`"1 mi=5280 ft"`
`"1 h=60 m"`

Each equality can make two conversion factors, which are equal to one.

`"1 mi"/"5280 ft"="1"="5280 ft"/"1mi"`

`"1 h"/"60 min"="1"="60 min"/"1 h"`

Multiply the given value by the conversion factor that has the desired unit in the numerator. This will leave you with the desired unit, and the undesired unit in the denominator will cancel.

Convert feet to miles.

`63756cancel"ft"xx(1"mi")/(5280cancel"ft")="12.075 mi"`

Convert minutes to hours.

`70cancel"min"xx(1"h")/(60cancel"min")="1.167 hour"`

Divide miles by hours.

`(12.075"mi")/(1.167"h")="10.3 mi/h"`

Sam's speed is about 10.3 mi/h.