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 ? .

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

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"#