Math  /  Algebra

QuestionA construction crew is lengthening a road. The road started with a length of 53 miles, and the crew is adding 4 miles to the road each day. Let LL represent the total length of the road (in miles), and let DD represent the number of days the crew has worked. Write an equation relating LL to DD. Then use this equation to find the total length of the road after the crew has worked 33 days.
Equation: \square
Total length of the road after 33 days: \square miles

Studdy Solution

STEP 1

1. The initial length of the road is 53 miles.
2. The crew adds 4 miles to the road each day.
3. LL represents the total length of the road in miles.
4. DD represents the number of days the crew has worked.

STEP 2

1. Write an equation relating LL to DD.
2. Use the equation to find the total length of the road after the crew has worked 33 days.

STEP 3

Identify the initial length of the road and the rate at which the length increases each day.
The initial length of the road is 53 miles, and the length increases by 4 miles each day.

STEP 4

Formulate the equation relating LL (total length) to DD (number of days).
Since the road starts at 53 miles and increases by 4 miles each day, the equation is:
L=53+4D L = 53 + 4D

STEP 5

Substitute D=33D = 33 into the equation to find the total length of the road after 33 days.
L=53+4×33 L = 53 + 4 \times 33

STEP 6

Perform the multiplication and addition to find the value of LL.
L=53+132 L = 53 + 132

STEP 7

Simplify the expression to find the total length of the road.
L=185 L = 185
Equation: L=53+4D L = 53 + 4D
Total length of the road after 33 days: 185 185 miles

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