CUSTOMARY UNITS OF LENGTH WORD PROBLEMS

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

Solved Problems

Problem 1 :

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 2 : 

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 3 : 

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 4 : 

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 5 : 

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. 

Problem 6 : 

After school Quentin walks his dog around a park. The park is a square with a side length of 450 feet. How far does Quentin have to walk his dog to cover the complete park ? 

Solution :

Distance needed to cover the complete park is  

=  Perimeter of the square park 

=  4a

=  4(450)

=  1800 feet 

So, Quentin has to walk 1800 feet to cover the complete park. 

Problem 7 : 

Joslin needs to put fence around a square vegetable garden with a side length of 8 yards. How many feet of fence does he need?

Solution :

Here information is given in yards and answer is expected in feet. 

So, convert yards into feet.

We now that, 

1 yard  =  3 feet

Then, we have

8 Yards  =  8  3 feet  =  24 feet

Therefore, length of each side of the garden is 24 feet. 

No. of feet of fence he needs is 

=  Perimeter of the square vegetable garden 

=  4a

=  4(24)

=  96 feet 

So, Joslin needs to put 96 feet of fence to cover the complete garden.

Problem 8 : 

Daniel has rectangle shaped room whose length is 20 feet and width is 15 feet. If carpet costs $2 per square foot, how much will it cost to carpet the room ?

Solution :

Area of the rectangle shaped room is 

=  length  width

=  20  15 

=  300 square ft. 

Given : Cost per square ft is $2. 

Then, the Cost for 300 square ft is 

=  300 ⋅ $2

=  $600

So, it will cost $600 to carpet the room.

Problem 9 :

Who is driving faster,

Lenin  covers 6 miles in 2 minutes

or 

Daniel covers 225 miles in 1.5 hours ?

Solution :

To compare the given measures, convert them in to unit rates in distance per hour. 

Lenin

Distance in 2 min :

=  6 miles

Distance in 1 min :

=  6/2

=  3 miles

1 hour  =  60 minutes

Distance in 1 hr :

=   60  3

=  180 miles

Daniel

Distance in 1.5 hrs :

=  225 miles

Distance in 1 hr :

=  225/1.5

=  150 miles

From the above unit rates, Lenin covers more miles than Daniel per hour. 

So, Lenin is driving faster.

Problem 10 :

Who is better in walking,

  Shanel walks 2/ 5 of a mile every 1/7 hour.  

or 

Declan walks 3/5 of a mile every 2/7 hour ?

Solution :

To compare the given measures, convert them in to unit rates in miles per hour (speed).

Speed  =  Distance / Time 

Shanel

Speed  =  (2/5)/(1/7)

=  (2/5)  (7/1)

=  14/5

=  2.8 miles per hour

Declan

Speed  =  (3/5)/(2/7)

=  (3/5)  (7/2)

=  21/10

=  2.1 miles per hour

From the above unit rates, Shanel walk more miles than Declan per hour. 

So, Shanel is better in walking.

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