Question

Joe and Amanda are digging a trench to lay pipe for a new sprinkler system. The information below shows how many meters they can dig per hour. Time (hours) 1 2 3 4 5 Distance (meters) 8.5 17 25.5 34 If the rate of meters per hour remains the same, how many meters can they dig in 5 hours? 39 meters

Answer 1

They dig 42.5 meters in 5 hours

Explanation:

The following information was given:

Time (hours) Distance (meters)

1 8.5

2 17

3 25.5

4 34

5 x

Finding x when the rate of meters per hour remains the same

Let us first find the rate in meters per hour

rate = change in distance ÷ change in time

Between 1 and 2 hours

`rate = (d_2 - d_1)/(t_2 - t_1) \\where:\\d_2 = 17 m\\d_1 = 8.5m\\t_2 = 2\ hours\\t_1 = 1\ hour\\\therefore\ rate = (17 - 8.5)/(2-1) \\rate =(8.5)/(1) \\rate = 8.5\ m/hr`

This means that for every additional 1 hour, 8.5 meters is dug

Finding the meters dug in 5 hours

4 hours = 34 meters

4 hours to 5 hours = 1 hour

for every additional 1 hour, 8.5 meters are dug

∴ 4 hours to 5 hours = 34 + 8.5

4 hours to 5 hours = 42.5 meters