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