Question

A construction crew is lengthening a road. The road started with a length of 53 miles, and the crew is adding 3 miles to the road each day. Let L represent the total length of the road (in miles), and let D represent the number of days the crew has worked. Write an equation relating L to D. Then use this equation to find the total length of the road after the crew has worked 31 days.

Answer 1

• L = 53 + 3D
• 146 miles

Explanation:

(a) At 3 miles per day, after D days, the added length is 3D miles. When that is added to the original length, the total length is ...

L = 53 + 3D . . . . miles

__

(b) When D=31, the length is ...

L = 53 + 3·31 = 53 +93 = 146 . . . . miles

Answer 2

a). L=53+3 D.... equation

b). Total length of the road after the crew has worked 31 days=146 miles

Explanation:

Step 1

Find an expression for calculating the total length of a the road as follows;

L=F+(M×D)

where;

L=total length of the road in miles

F=starting length of the road in miles

M=number of miles per day added

D=number of days the crew has worked

In our case;

L=unknown

F=53 miles

M=3 miles per day

D=unknown

L=53+(3×D)

L=53+3 D.... equation

Solve for L when D=31 days

L=53+(3×31)

L=53+93=146

Total length of the road after the crew has worked 31 days=146 miles