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Question 174234: I am doing a practice test for a nursing entrance exam: If sally can paint a house in 4hrs, and john can paint the same house in 6hrs. How long will it take for both of them to paint the house together?
H=4
j=6 4+6=10 10/2=5 so 2hrs and 30min. the real answer is 2hrs and 24 min.
Please show me HOW TO FORMULATE my answer, because i am good at math, but this ? has me stumped by the answer.
A different problem, but the same type of ?: jim can fill a pool carrying buckets of water in 30min. sue can do the same job in 45 min. tony can do the same job in 1 1/2 hrs. how quickly can all 3 fill the pool together?
j=30m
s=45m
t=90m 30+45+90=165 165/3=55 avg of min. 55/3=18.1... so about 18min
...but the real ans is 15min. again, could you please show me HOW TO GET THE ANSWER, and what is the formal name for this type of word problem, so i could look up further info about it on the web. thanks
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Here's one approach to these types of problems:
Find the "rate" at which each person can do the job.
For the house-painting job, we'll find how much of the house can be painted by each participant in 1 hour.
If Sally can paint the house in 4 hours, then she can paint 1/4 of the house in 1 hour.
If John can paint the house in 6 hours, then he can paint 1/6 of the house in 1 hour. So, together, they can paint 1/4 + 1/6 = 5/12 of the house in 1 hour.
If the two of them can paint 5/12 of the house in 1 hour, then it will take them 12/5 hours to paint the house.
12/5 = 2 2/5 hours = 2 hours and 24 minutes.
Similarly for the second problem, find the "rate" at which each person can fill the pool.
Jim can fill the pool in 30 minutes, so he can fill 1/30 of the pool in 1 minute.
Sue can fill the pool in 45 minutes, so she can fill 1/45 of the pool in 1 minute.
Tony can fill the pool in 90 minutes (1 1/2 hrs), so he can fill 1/90 of the pool in 1 minute.
Working together, they can fill (1/30 + 1/45 + 1/90 = 6/90 = 1/15) of the pool in 1 minute, so it would take them 15/1 = 15 minutes to fill the pool together.
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