How do I solve this math problem?

Question

I've been studying for my high school entrance exam, and I know all the types of questions except for this. It's showing up a lot in the practice tests so I think I really need to know how to solve it.

Example:

If Martha can paint a house in 4 hours, and Jack can paint the same house in 3 hours, while Max can paint the house in 5 hours, how much time would be spent if they painted the house together?

Test is tomorrow morning so please answer ASAP.

Answer 1

Think of it this way:

In one hour,
Martha will be 1/4 = 25% done;
Jack will be 1/3 = 33% done; and
Max will be 1/5 = 20% done.

Thus, if they all work together, in one hour they will be 1/4 + 1/3 + 1/5 = 47/60 = 78% done. Thus, to finish the job it will take 60/47 hours, which is about 1 hour, 16 minutes, and 36 seconds.

Answer 2

I think the best way to solve a problem like this is to reason as follows:

In one hour, Martha can paint 1/4 of a house, Jack can paint 1/3 of a house, and Max can paint 1/5 of a house. So, working together, in one hour they can paint 1/4 + 1/3 + 1/5 of a house, or 47/60 of a house, and it will take 60/47 hours to paint the whole house.

Answer 3

the trick is always in how to set the problem up

Martha paints 1/4 house/hour
Jack paints 1/3 house/hr
Max paints 1/5 house/hr

therefore
(1/4 + 1/3 +1/5) = I house painted hour
47/60 of a house painted per hour
divide 47 into 60 = 1.28 hours

1 hr 17 minutes

Answer 4

Lets see how much of a house they can paint together in one hour.

Martha can paint a house in 4 hours, so she paints 1/4 of a house in an hour
Jack can paint a house in 3 hours, so he paints 1/3 of a house in an hour
Max can paint a house in 5 hours, so he paints 1/5 of a house in an hour.

1/4+1/3+1/5=15/60+20/60+12/60=47/60, so they paint 47/60ths of a house together.

At this pace, it will take 13/47ths of an hour to paint the remainder, so the total time is 1 and 13/47ths hour, or 60/47 hour.

(That's roughly 1 hour and 16.6 minutes, if it helps)

Answer 5

Martha does 1/4 the job per hour, Jack 1/3 and Max 1/5. If they are all working together, they do:

1/4 + 1/3 + 1/5 of the job per hour. Common denom is 60

15/60 + 20/60 + 12/60 = 47/60 of the job per hour.

To complete the job, find time t such that

(47/60)*t = 1

t = 60/47 hours

Answer 6

You add the rates.
martha's rate is 1/4 of a house/hr
jacks is 1/3 &
max is 1/5

working together the rate is
1/4+1/3+1/5=(15+20+12)/60=47/60 house/hr
painting 1 house will take 60/47 hrs=1 hr 16 min 36 sec

Answer 7

It takes 4 hours for Martha to paint the house, so:
4M=H; that is, 4 hours of martha working equals a painted house.
3J=H; 3 hours of jack working equals a painted house
5A=H; 5 hours of Max working equals a painted house.

Adding M+J+A, as we are combining all their working efforts:

H/4 +H/3 +H/5=xH
x is the number of hours it takes for them all combined, H is a completed house. In other words, all three's efforts times their total working hours equals a painted house.

Therefore x= 1/4+1/3+1/5, and works out as 47/60 hours. This is 47 minutes, as an hour can be separated into 60 minutes.

Hope this helps.

Answer 8

martha can paint 1/4 of the house in 1hr
jack can paint 1/3 of the house in 1hr
max can paint 1/5 of the house in 1hr

in 1hr (1/4 + 1/3 + 1/5)=.783 of the house is painted
in order to get the time necessary to paint the entire house you must multiply by the reciprocal

1= .783x
1( 1/.783) = x
x=1.278 hr= 1hr 16min

Answer 9

rate*time = work (rt= w)
m = martha's rate
j = jack's rate
x = max's rate
m = 1/4
j = 1/3
x = 1/5

(1/4+1/5+1/3) * n = w

(15/60 + 12/60 + 20/60) * n = w
47/60 *n = w
60/47 hours = 1.277 hours

Answer 10

4+3+5 = 12
12/3=4 hours average for each to complete the job alone.
4 hours/3 persons= 1.333 (.333*60=20 minutes) or 1 hour and 20 minutes.

I like to use decimals in my calculations, the 1 hr and 16.6 minute answers are from those using fractions, so it is a rounding difference. 19.999999 minutes to 20.