Question

a crew is building a sidewalk. it can build a length of 3 kilometers in 5 days. at this rate, what length sidewalk can it build in 35 days?
(a) let ( l ) be the unknown length of sidewalk the crew can build (in kilometers). using the values below, create a proportion that can be used to find ( l ).
values: ( l ), ( 3 ), ( 5 ), ( 35 )
( \frac{square}{square} = \frac{square}{square} )
(b) use the proportion from part (a) to find the length of sidewalk the crew can build in 35 days. do not round any computations.
( square ) kilometers

Explanation:

Part (a)

Step1: Identify the ratio

The rate of building is constant, so the ratio of length to days should be equal. The length built in 5 days is 3 km, and the length built in 35 days is \( L \) km. So the proportion is \(\frac{\text{Length}}{\text{Days}}\) for both cases.

Step2: Form the proportion

So we have \(\frac{L}{35}=\frac{3}{5}\) (or also \(\frac{3}{5}=\frac{L}{35}\) is correct too, as proportion can be set either way as long as the ratios are of length to days).

Step1: Cross - multiply the proportion

From \(\frac{L}{35}=\frac{3}{5}\), cross - multiplying gives \(5\times L = 3\times35\).

Step2: Solve for \(L\)

Calculate \(3\times35 = 105\), so \(5L=105\). Then divide both sides by 5: \(L=\frac{105}{5}\).

Step3: Simplify the division

\(\frac{105}{5}=21\).

Answer:

\(\boldsymbol{\frac{L}{35}=\frac{3}{5}}\) (or \(\frac{3}{5}=\frac{L}{35}\))

Part (b)