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How do I solve this problem, please?
Person A can paint a house in 4 hours, and person B can paint the same house in 6 hours. Together how long will it take them to paint the house? Answer in the practice test key is 2 hours and 24 minutes. How is this answer derived? What type of algebraic formula is used here?j Thanks very much for your help.
Hello Liz,
We know that Work=Rate x Time, and
Person A has a rate of 1 job in 4 hrs, or 1/4 of a job/hr.
Person B has a rate of 1 job in 6 hrs, or 1/6 of a job/hr.
Let T=the time required if they work together. If they work
together, their combined rate is 1/4 + 1/6 = 5/12 job/hr.
Thus, (5/12)xT=1 (i.e. 1 job), hence T=12/5 hrs = 2.4 hours,
which is 2 hrs 24 minutes.
OK? I hope this helps! :-)
Abe
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| Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |
| Comment | Perfect clear answer. Thanks. I didn't know the formula before now and this will be very helpful to me in my job as a project manager. Often I have to add an additional resource to a task and re-estimate the duration. | ||
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Answers by Expert:
Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience
Over 15 years teaching at the college level.
Organizations belong to
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
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