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Question 1087986: Jessie and Mark are planning to paint a house together. Jessie thinks that if he works alone, it would take him 5 hours more than the time Mark takes to paint the entire house. Working together, they can complete the job in 6 hours.
QUESTION: How will you solve the equation formulated? What mathematics concepts and principles are you going to use?
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Let m = the amount of time required by Mark to paint the entire house alone
Thus, their rates of painting will be 1/m and 1/(m+5) houses per hour
Working together their combined rate is:
1/m + 1/(m+5) = 1/6 [houses per hour]
The above expression tells us how much of the house they complete every hour working together
Solve for m:
m^2 + 5m = 12m + 30
m^2 - 7m - 30 = 0
Factor:
(m-10)(m+3) = 0
Take the positive solution, m = 10 [hours]
So Mark's rate of painting is 1/10 houses per hour and Jessie's rate is 1/15 houses per hour.
If it's confusing, take a simple example. Suppose someone can perform a task, say clean their room, in 2 hours.
That means they can clean 1/2 of their room every hour [this is their rate of working]
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