G8 M4 L25 HW: Linear Equations of Constant Rates
1a.) Train A can travel a distance of 500 miles in 8 hours. Assuming the train travels at a constant rate, write a
linear equation that represents this situation.
500 ÷ 8 = 62.5
y = 62.5x
1b.) If the figure below represents the constant rate of travel for Train B, then which train is faster? Explain.
Train A: 62.5 miles per hour
Train B: 200 ÷ 3 = 66.7 miles per hour
Train B is faster because it has a larger slope.
2a.) Natalie can paint 40 square feet in 9 minutes. Assuming she paints at a constant rate, write a linear equation
that represents the situation.
40 ÷ 9 = 4.4
y = 4.4x
2b.) The table of values below represents the area painted by Steven for a few selected time intervals. Assume
Steven is painting at a constant rate. Who paints faster? Explain.
Minutes (𝑥)
Area Painted (𝑦)
3
10
5
50
3
Steven: 10 ÷ 3 = 3.3 square feet per minute.
6
20
Natalie paints faster because she has a higher slope.
8
80
3
Natalie paints at a rate of 4.4 square feet per minute.
3a.) Bianca can run 5 miles in 41 minutes. Assuming she runs at a constant rate, write the linear equation that
represents the situation.
5 ÷ 41 = 0.12 miles per minute
3b.) The figure below represents Cynthia’s constant rate of running. Who runs faster? Explain.
1 ÷ 7 = 0.14 miles per minute
Cynthia runs faster because she has a higher constant rate.
4a.) Geoff can mow an entire lawn of 450 square feet in 30 minutes. Assuming he mows at a constant rate, write
the linear equation that represents this situation.
450 ÷ 30 = 15 square feet per minute
y = 15x
4b.) The figure below represents Mark’s constant rate of mowing a lawn. Who mows faster? Explain.
14 ÷ 2 = 7 square feet per minute
Geoff mows faster because he has a higher rate.