word projlem

Question

the new mechanic at speedy lube can perform thirty oil changes in 4 hours.His assistant  can perform the same number of oil changes in 6 hours.How long would it take them to do the work together?

Answer 1

Hi Jeffrey!

 

Let m be the rate the mechanic can work, and let a be the rate his assistant can work.

 

We use the equation that

 

rate = amount of oil changes completed/time 

 

We can write m = 30/4 = 7.5 and a = 30/6 = 5.

 

Next, find m + a = 12.5.

 

Lastly, find 30/m +a = 30/12.5 = 2.4 hours.

 

I hope is helpful.

 

Best regards!

Answer 2

mechanic takes 4 hours, so he does 1/4 of the job in 1 hour

assistant takes 6 hours, so he does 1/6 of the job in 1 hour

x=# of hours working together

(1/4)(x)+(1/6)(x)=1 (job done)

multiply both sides by 12

3x+2x=12

5x=12

x=12/5=2.4 hours together

another way of looking at the problem...

30 changes in 4 hours (240 minutes) is 1 change every 8 minutes

30 changes in 6 hours (360 minutes) is 1 change every 12 minutes

the LCM of 8 and 12 is 24

every 24 minutes (24/8=3 and 24/12=2) 5 changes are done

30/5=6, 6*24=144 minutes=2 hours 24 minutes=2.4 hours