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Name: Stephanie
Level of question: grade 6 level
Person asking question: student
Dear Math Central,
My grade 6 class and I have been having a hard time with this question. We thought we had the answer, but when our teacher checked it in her manual, it was wrong. Please help us!
Here is the question:
Tom takes 10 hours to piant a mural on the wall of Evergreen School. Carol takes 6 hours to do the same job. If they work together, how long will it take them to paint the mural?
Please get back to me soon!
Thank you,
Stephanie
Hi Stephanie,
Think in terms of the rates at which they work. Tom paints a mural in 10 hours so he paints one-tenth of a mural per hour. Carol paints a mural in 6 hours so she paints one-sixth of a mural per hour. Hence, working together they paint at the rate of
1/10 + 1/6 = 8/30 = 4/15 of a mural per hour.
At this rate, how long does it take them to paint one mural?
Another approach is to use the least common multiple of 6 and 10, that is 30.
In 30 hours, How many similar murals could
Tom paint? How many murals could Carol paint? So, what is the total
number of murals that they could paint in 30 hours? How long do they
take to paint one mural?
Cheers,
Claude and Penny
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