CUSTOMARY UNITS OF LENGTH

About "Customary units of length"

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

For measuring length, the U.S. customary system uses the inch, foot, yard and mile which are the only four customary length measurements in everyday use.

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

Customary units of length - Conversion

Customary units of length - Practice problems

Problem 1 :

Convert 2 feet into inches.

Solution :

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

2 feet = 2 x 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 x 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

Customary units of length - Word problems

Problem 1 :

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

Solution :

Distance covered in 2 hours = 60 miles

Distance covered in 1 hour = 30 miles

We know that 1 hour = 60 minutes and 1 mile = 1760 yards

1 hour -----> 30 miles =====> 60 minutes -----> 30 x 1760 yards

60 minutes -----> 52800 yards

So, distance covered in 60 minutes = 52800 yards

Distance covered in one minute = 52800 / 60 yards

= 880 yards

Hence 880 yards of distance covered in 1 minute.

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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

Hence the speed of Mark is 352 feet per minute.

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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 bigger unit (foot). So we have to divide.

Since we divide, we have to use the fraction 1/12.

Because, 1 foot = 12 inches

9 inches = 9 x 1/12 ft

9 inches = 3/4 ft

Hence 9 inches is equal to 3/4 ft.

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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 :

Height of the television = 24 inches

Height of the stand = 3 feet = 3 x 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

Hence the top of the television is 60 inches far from the floor.

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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 x 5280 feet = 10560 feet

Therefore,

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

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

Difference between (1) and (2) ----> 10560 - 10000 = 560 feet

Hence Becky ran farther by 560 feet.

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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

Hence Quentin has to walk 1800 feet to cover the complete park.

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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, let us convert yards into feet.

8 Yards = 8 x 3 feet = 24 feet

Therefore, length of each side of the garden = 24 feet

No. of feet of fence he needs is

= Perimeter of the square vegetable garden

= 4a

= 4(24)

= 96 feet

Hence Joslinh needs to put 96 feet of fence to cover the complete garden.

Let us look at the next word problem on "Customary units of length"

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 = length x width

= 20 x 15

= 300 square ft.

Cost per square ft = $2

Cost for 300 square ft = $2 x 300

Cost for 300 square ft = $600

Hence it will cost $600 to carpet the room.

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Problem 9 :

Who is driving faster,

Lenin covers 6 miles in 2 minutes

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 = 3 miles

1 hour = 60 minutes

Distance in 1hr = 60x3

Distance in 1 hr = 180 miles

Daniel

Distance in 1.5 hrs =225 miles

Distance in 1 hr = 225 / 1.5

Distance in 1 hr = 150 miles

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

Hence, Lenin is driving faster.

Problem 10 :

Who is better in walking,

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

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)

Speed = (2/5) x (7/1)

Speed = 14 / 5

Speed = 2.8 miles per hour

Declan

Speed = (3/5) / (2/7)

Speed = (3/5) x (7/2)

Speed = 21 / 10

Speed = 2.1 miles per hour

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

Hence, Shanel is better in walking

After having gone through the problems explained above, we hope that the students would have understood the stuff given on "Customary units of length".

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