Question

You are scheduled to start your job at an oil change shop 2 hours after the shop opens. Two hours after you start, a total of 11 cars have had their oil changed since the shop opeaned. Three hours later, a total of 14 cars had have their oil changed.At what rate are cars getting their oil changed since you started working? How many cars had their oil changed before you started work?

Answer 1

shop opens - open shop time zero

you start working - open shop time is 2 hrs

2 hrs after you start - open shop time is 4 hrs - 11 cars done

3 hrs later - open shop time 7 hours - 14 cars done

From 4 hrs since the shop opened till 7 hours since the shop opened, you were working that entire time. 14 - 11 cars = 3 cars. 7 hours - 4 hours = 3 hours.

(3 cars)/(3 hours) = 1 car/hour

With you working, the rate is 1 car per hour.

You started working at the shop's 2 hours of operation. You worked until the shop's 7 hours of operation. You worked 7 hrs - 2 hrs = 5 hrs.

Since the rate of cars per hour while you work is 1 car/hour, then during the 5 hours you worked, 1 car/hour * 5 hours = 5 cars.

5 cars got done while you were working.

Since 14 cars got done in 7 hours, then 14 cars - 5 cars = 9 cars.

9 cars were done before you started.

Answer 2

The cars are getting their oil changed at a rate of 1 car per hour.

9 cars had their oil changed before you started work.

Explanation:

We have been given that you are scheduled to start your job at an oil change shop 2 hours after the shop opens. Two hours after you start, a total of 11 cars have had their oil changed since the shop opened. Three hours later, a total of 14 cars had have their oil changed.

We have two points on line (4,11) and (7,14). We will find the slope of line passing through these points.

`m=(y_2-y_1)/(x_2-x_1)`

`m=(14-11)/(7-4)`

`m=(3)/(3)`

`m=1`

Since slope of line is 1, therefore, the cars are getting their oil changed at a rate of 1 car per hour.

Since you 11 cars are oiled when you worked two hours and rate of oil changing is 1 car per hour, so you will change oil of two cars in two hours.

`11-2=9`

Therefore, 9 cars had their oil changed before you started work.