Question

A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked. Suppose that x and y are related by the equation y=53 + 2x. Answer the questions below. Note that a change can be increased or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was the road’s length when the crew started working?What is the change per day in the road’s length?

Answer 1

Given the equation:

`y=53+2x`

Where y represents the total length of the road (in miles), and x represents the number of days the crew has worked.

(a) What was the road’s length when the crew started working?

When the crew started working we have x = 0. Then:

`\begin{gathered} y=53+2\cdot0 \\ \therefore y=53\text{ miles} \end{gathered}`

The road's length is 53 miles.

(b) What is the change per day in the road’s length?

The change per day in the road's length is 2 miles/day.