Word Problem Wednesday: A Mad Man With A Box

Meet The Doctor. Doctor who, you say? The Doctor. Just The Doctor. He is a madman with a box. By madman, we mean, of course, the last living Time Lord from the planet Gallifrey, who lives to travel across space and time and explore and save people. The box is a T.A.R.D.I.S. - Time and Relative Dimension in Space - his spaceship. Stuck disguised as a blue Police Telephone Box. While the Doctor's space physics and science are not real (at least to our ignorant human brains) - 

...Right. Anyways, while The Doctor messes around with science that is beyond our current understanding, his companions, Rose and Mickey, are Earth-bound trying to fix up Rose's totally normal car. See if you can solve this week's word problem challenge!

Challenge Question: Mickey, the mechanic, can replace the tires on Rose's car in 20 minutes. His friend, Noel, can replace the tires in 25 minutes. If they work together, and only one person can work on a tire at a time, how long will it take them to replace all 4 tires on Rose's car?

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The Doctor is busy installing a time vortex in the engine of Rose's car. 

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He's using experimental Time Lord technology (bigger on the inside).

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Ready for the answer? 

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Answer: Either 12 ¹/₂ or 12 minutes, depending on how you solve the problem

Solution: There are two ways to solve this problem. First, Mickey and Noel can each replace half of the wheels. Mickey can replace 4 wheels in 20 minutes, so he can replace 2 wheels in 10 minutes. Noel can replace 4 wheels in 25 minutes, so he can replace 2 wheels in 12 ¹/₂ minutes. If they work at the same time, they’ll be done in 12 ¹/₂ minutes. Alternatively, we can find out how long it would take them if Mickey takes over for Noel after 10 minutes, at which point Noel will be 10 ÷ 12 ¹/₂ = ⁴/₅ done with his half of the tires. Since Mickey can finish 2 tires in 10 minutes, he can finish the remaining 1/5 of Noel’s work in ¹/₅ × 10 = 2 minutes. So, if Mickey takes over, they can get the job done in 12 minutes.

Looking for some more math fun? Call us at Mathnasium of Cave Creek!