Question

The speed of sound is 1,088 feet per second. Convert the speed of sound to miles per hour. Round your answer to the nearest whole number ? .

Answer 1

About `742` miles per hour, `741.` `bar81` to be exact

Explanation:

You can solve this by using dimensional analysis. Write what you have down:

`1088` ft`/ 1` sec

To use dimensional analysis, you want to get rid of the current units and end up with the next.
There are `5280` ft in a mile (mile because that is the unit you want to change to). Since you can only cross out something in the numerator with something in the denominator, you place `5280` ft in the denominator.

`1088` ft`/`1`sec`*``5280# ft

Since you cannot change the value of the equation, make sure to add 1 mile in the top.

`1088` ft`* 1` mi/ `1` ``sec`` `*` `5280` ft

`1088` `cancel (ft)` `1` #`mi/`1 `sec``` #`5280` `cancel (ft)`

Now you have miles per second. Since you are looking for miles an hour, and the seconds are at the bottom, you need to add how many seconds in 1 hour in the numerator.
There are 3600 seconds in an hour.

`1088` `* 1` mi `* 3600` sec/ `1` sec `*5280` `*1` hr

The seconds cross out.

`1088` `* 1` mi `* 3600` `cancel(sec)`/ `1` `cancel(sec)` `*5280` `*1` hr

Multiply and get `~~742` mi / hr

Answer 2

The speed of sound in mi/h is `741.bar(18)` `"mi/h"`.

Explanation:

Use dimensional analysis. First write the equalities between feet and miles, and seconds and hours.

Feet to miles

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

Conversion factors

`"5280 ft"/"1 mi"` and `"1 mi"/"5280 ft"`

Seconds to hours

`"3600 s"` `=` `"1 h"`

Conversion factors

`"3600 s"/"1 h"` and `"1 h"/"3600 s"`

Given

`"1088 ft/s"` `rarr` `"? mi/h"`

Multiply by the given speed by the conversion factors that cancel feet and seconds.

`(1088color(red)cancel(color(black)("ft")))/(1color(blue)cancel(color(black)("s")))xx(1"mi")/(5280color(red)cancel(color(black)("ft")))xx(3600color(blue)cancel(color(black)("s")))/(1"h")` `=` `741.bar(18)` `"mi/h"`