SOLUTION: Could you please help me figure out the answer to this word problem? If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take f

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Could you please help me figure out the answer to this word problem? If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take f      Log On


   

Question 323259: Could you please help me figure out the answer to this word problem?
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
A. 2 hrs and 24 mins
B. 3 hours and 12 mins
C. 3 hours and 44 mins
D. 4 hours and 10mins
E. 4 hours and 33 mins.
I thought that the way to get the answer would be to add both times together (4+6=10) and divide by two (the number of people painting), to get 5hrs as the answer. Apparently this is not correct, since 5 hrs is not one of the answers.
Thanks for helping.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"If Sally can paint a house in 4 hours", then she can paint 1%2F4 of the house in 1 hour (divide each number by 4). So Sally's rate is 1%2F4 of a house per hour. Likewise, since "John can paint the same house in 6 hours", he can paint 1%2F6 of the house in one hour. So his rate is 1%2F6 of a house per hour.


Now add the two rates to get: 1%2F4%2B1%2F6=3%2F12%2B2%2F12=5%2F12


So their combined rate (if conditions are perfect) is 5%2F12 houses per hour. In other words, together they can paint 5%2F12 of the house in one hour.


Now let 't' be the time that it takes them to complete the task. If we multiply the rate 5%2F12 by the time 't', we will get a complete job. This is simply denoted by 1 (since we want to paint one house).


Basically, we then get the equation %285%2F12%29t=1


%285%2F12%29t=1 Start with the given equation.


cross%2812%29%285%2Fcross%2812%29%29t=1%2A12 Multiply both sides by 12.


5t=12 Multiply and simplify


%28cross%285%29t%29%2Fcross%285%29=12%2F5 Divide both sides by 5.


t=12%2F5 Simplify


So working together, they can paint 1 house in t=12%2F5 hours. Convert it to a mixed fraction to get 12%2F5=2%262%2F5. Finally, multiply 2%2F5 by 60 (to convert it into minutes) to get 60%282%2F5%29=120%2F5=24. So 12%2F5 or 2%262%2F5 hours is 2 hours and 24 minutes.


So they can paint the house in 2 hours and 24 minutes. This means that the answer is A. 2 hrs and 24 mins