PLEASE HELP!!!! 44 ft/sx1 mi/5,280 ft x 3,600 s/h?

Question

Evaluate the following and be sure to use proper units.

44 ft/sx1 mi/5,280 ft x 3,600 s/h

This is has totally stumped me I have gone over my lesson plan and I am just lost!!! Please anyone I need some guidance!

Answer 1

It looks like this is an expression that converts 44 ft/sec into units of miles per hour.

The idea is that you are multiplying three fractions here. When you multiply fractions that contain units (like feet, miles, seconds, and hours), you can cancel out the units the same way you would cancel out common divisors.

This means that the "ft" in the numerator of "44 ft/s" will cancel with the "ft" in the denominator of "1 mi/5280 ft". Likewise, the "s" in the denominator of the first fraction cancels the "s" in the numerator of the 3rd fraction. So after canceling those units, what you end up with is this:

(44/1) x (1 mi/5280) x (3600/h)

The answer you get will have "mi" in the numerator, and "h" in the denominator, so it will be expressed in "mi/h" (i.e., miles per hour).

Notice that the fraction "1 mi/5280 ft" is just the same as "1". This is true because its numerator equals its denominator. For the very same reason, "3600 s/hr" is also the same as "1". So you are really multiplying "44 ft/s" times "1" times "1". This assures you that the answer you get will be equivalent to "44 ft/s", even though the final units will be different.

Answer 2

Hi,

44 feet....1 mile....3,600 sec
----------.x.---------.x.------------- =
1 sec......5280ft....1 hour

The units of feet and seconds cancel out, leaving miles per hour


44 ...1 mile....3,600
----.x.---------.x.------------- =
1 ......5280....1 hour

Multiplying these fraction together and reducing gives:

30 miles/hour <== answer

I hope this helps!! :-)

Answer 3

(44 ft/s)(1mi/5280 ft)(3600 s/h) = (44)(3600)/(5280) mph
= 30 mph