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Zorluk: ZorUS Customary Linear Measurements

A construction crew has a spool containing exactly 14\frac{1}{4} mile of underground cable. They use 12023120 \frac{2}{3} yards of the cable for their first trench and 412412 feet 88 inches of the cable for their second trench. How much cable remains on the spool?

  1. 545 feet 4 inchesCevap
  2. B
    450 feet
  3. C
    786 feet 8 inches
  4. D
    545 feet 2 inches

Cevap

545 feet 4 inches
To find the remaining cable, all measurements must be converted to a common unit. First, find the total cable in feet: since 1 mile=5280 feet1 \text{ mile} = 5280 \text{ feet}, 14 mile=1320 feet\frac{1}{4} \text{ mile} = 1320 \text{ feet}. Next, convert the first trench length to feet: 12023 yards×3 feet/yard=362 feet120 \frac{2}{3} \text{ yards} \times 3 \text{ feet/yard} = 362 \text{ feet}. The second trench is 412 feet 8 inches412 \text{ feet } 8 \text{ inches}. The total used is 362 feet+412 feet 8 inches=774 feet 8 inches362 \text{ feet} + 412 \text{ feet } 8 \text{ inches} = 774 \text{ feet } 8 \text{ inches}. Finally, subtract this from the starting amount. Borrowing 1 foot1 \text{ foot} (12 inches12 \text{ inches}) from 1320 feet1320 \text{ feet} gives 1319 feet 12 inches1319 \text{ feet } 12 \text{ inches}. Subtracting the used cable gives 1319−774=545 feet1319 - 774 = 545 \text{ feet} and 12−8=4 inches12 - 8 = 4 \text{ inches}.

Adım Adım Çözüm

1
Convert the total cable length from miles to feet.
14×5280=1320\frac{1}{4} \times 5280 = 1320 feet.
Standardizing all measurements to the same base unit (feet) is required before adding or subtracting.
2
Convert the length used for the first trench from yards to feet.
12023×3=362120 \frac{2}{3} \times 3 = 362 feet.
There are 3 feet in a yard, so multiplying the mixed fraction by 3 gives the exact length in feet.
3
Calculate the total amount of cable used for both trenches.
362 feet+412 feet 8 inches=774 feet 8 inches362 \text{ feet} + 412 \text{ feet } 8 \text{ inches} = 774 \text{ feet } 8 \text{ inches}.
Adding the individual segments provides the total length that must be subtracted from the spool.
4
Subtract the total used cable from the total spool length.
1320 feet−774 feet 8 inches=545 feet 4 inches1320 \text{ feet} - 774 \text{ feet } 8 \text{ inches} = 545 \text{ feet } 4 \text{ inches}.
To subtract the 8 inches, borrow 1 foot (12 inches) from 1320 feet to make it 1319 feet 12 inches. Subtracting yields 1319−774=5451319 - 774 = 545 feet and 12−8=412 - 8 = 4 inches.

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Multi-step conversion and arithmetic using US Customary linear measurements
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US Customary Linear Measurements

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