CUSTOMARY UNITS OF LENGTH

Customary units of length is a system of measurements commonly used for length in the united states. 

Word problems given in this section will be much useful for the students who would like to practice problems on customary units of length like inch, foot, yard and mile

For measuring length, the U.S. customary system uses the which are the only four customary length measurements in everyday use. 

The relationship among the measurements inch, foot, yard  and mile  are given below.

12 inches  =  1 foot

3 feet  =  1 yard

5280 feet  =  1 mile

1760 yards  =  1 mile

Problem 1 :

Convert 2 feet into inches. 

Solution :

Here, we convert bigger unit into smaller unit. So we have to multiply.

2 feet  =  2 ⋅ 12 inches 

2 feet  =  24 inches

Hence, 2 feet is equal to 24 inches.

Problem 2 :

Convert 3.5 yards into inches. 

Solution :

Here, we convert bigger unit into smaller unit. So we have to multiply.

3.5 yards  =  3.5 ⋅ 36 inches

3.5 yards  =  126 inches

Hence, 3.5 yards is equal to 126 inches.

Problem 3 :

Convert 30 inches into feet. 

Solution :

Here, we convert smaller unit into bigger unit. So we have to divide.

30 inches  =  30/12 feet 

30 inches  =  2.5 feet

Hence, 30 inches is equal to 2.5 feet.

Problem 4 :

Convert 5280 yards into miles. 

Solution :

Here, we convert smaller unit into bigger unit. So we have to divide.

5280 yards  =  5280/1760 miles 

5280 yards  =  3 miles

Hence, 5280 yards is equal to 3 miles.

Problem 5 :

Convert 24 feet into yards 

Solution :

Here, we convert smaller unit into bigger unit. So we have to divide.

24 feet  =  24/3 yards 

24 feet  =  8 yards 

Hence, 24 feet is equal to 8 yards.

Problem 6 : 

David travels 60 miles in two hours. How many yards of distance will he cover in one minute ? 

Solution :

We know that, 

1 hour  =  60 minutes

1 mile  =  1760 yards

Given : Distance covered in 2 hours is 60 miles. 

Then, we have

Distance covered in 1 hour  =  30 miles

Distance covered in 1 hour  =  30 ⋅ 1760 yards

Distance covered in 60 minutes  =  30 ⋅ 1760 yards

Distance covered in 60 minutes  =  52800 yards

Distance covered in 1 minute  =  52800/60 yards 

Distance covered in 1 minute  =  880 yards

So, David will cover 880 yards of distance in 1 minute.

Problem 7 : 

Mark jogged 15840 feet in 45 minutes. Find the speed of Mark in feet per minute. 

Solution :

Speed  =  Distance/Time

Speed  =  15840/45

Speed  =  352 feet per minute

So, the speed of Mark is 352 feet per minute. 

Problem 8 : 

Use a fraction to find the length in feet of a shoe that is 9 inches long. 

Solution :

Here, we convert smaller unit (inches) into larger unit (foot).

So we have to divide.

Because, 1 foot  is  equal 12 inches, we have to use the fraction 1/12.

9 inches  =  9 ⋅ 1/12 ft

9 inches  =  3/4 ft

So, the length of the shoe is 3/4 ft. 

Problem 9 : 

Kevin has a new television that is 24 inches tall. If Kevin sets the television on a 3-foot-tall stand, how far from the floor will the top of the television be (in inches) ?

Solution :

Given : Height of the television is 24 inches. 

Height of the stand is

=  3 feet

=  3 ⋅ 12

=  36 inches

Distance from the floor to the top of the television is 

=  Height of the stand + Height of the television

=  36 + 24 

=  60 inches

So, the top of the television is 60 inches far from the floor. 

Problem 10 : 

Becky and Keith each ran for exactly 20 minutes on a treadmill. Keith’s treadmill said he had run 10,000 feet. Becky’s treadmill said she had run 2 miles. Who ran farther, and how much farther?

Solution :

Both Becky and Keith took the same amount of time. That is 20 minutes.

Distance covered by Becky and Keith are given in different units. (Miles and Feet)

We have to make the units to be same. 

Let us convert miles in to feet. 

So,

2 miles  =  2 ⋅ 5280 feet

2 miles  =  10560 feet 

Therefore,

Distance covered by Becky  =  10560 feet -----(1) 

Distance covered by Keith  =  10000 feet -----(2)

Difference between (1) and (2) is 

=  10560 - 10000

=  560 feet

So, Becky ran farther by 560 feet. 

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