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# Basic Math/math

Question
The Yellow Cab company wants to keep its cars in good operating condition.  Oil is changed once every 6 weeks.  Brakes are inspected and repaired every 10 weeks.
a. After a new cab is put in service, how many weeks will pass before the cab is due for both an oil change and brake inspection? When will be the second time?
b. Suppose the oil change time is changed to 8 weeks and the brake inspection to 12 weeks.  How many weeks will pass before the cb is due for both an oil change and a brake inspection?

To solve a problem like this, you can do a quick write-up on a piece of paper, detailing this particular company's maintenance schedule.

Oil is changed every six weeks, and brakes are fixed every ten. We need to know when the two dates will intersect. So, oil is changed in week 6. Next, oil is changed in week 12, followed by weeks 18, 24, and 30. Brakes are done in weeks 10, 20, and then 30.

If you do a "write-up," such as this, you'll see that the first time that an oil change and brake repair is scheduled will be during the thirtieth week.

A simpler way is just to list the multiples for 6 and 10. For 6, you have 6, 12, 18, 24, 30, 36, 42, 48, etc. For 10, you have 10, 20, 30, 40, 50, 60, etc.

The least common multiple is 30. If you expanded the lists, you'd see that the second time both an oil change and brake repair were scheduled would be the sixtieth week.

The second part of the problem is solved the same way as the first. Though instead of finding the least common multiple of 6 and 10, you need to find it for 8 and 12. For 8, you have 8, 16, 24, 32, 40, etc. For 12, you have 12, 24, 36, 48, 60, etc. The least common multiple here is 24, so this would take place in the 24th week.

Hope this helps.

Regards,
John

Basic Math

Volunteer

#### John Zalewski

##### Expertise

I can help you solve problems involving fractions, decimals, ratios, and algebra. I can teach you how to do math faster, and even in your head. I can teach math definitions, and help you study, if necessary. Please do not ask any graphing, trigonometry, or calculus questions. Try to work through homework questions before asking for assistance.

##### Experience

I routinely process numbers of all kinds in my head, without need of a calculator.

Education/Credentials
I was an A math student while in high school.