Two people are painting a house...?

Question

Jack can paint a house in 4 hours; Jill can does a house in 6 hours. How long does it take if they paint a house together???

I tried many ways of figuring this out but i haven't yet...thanks!

Answer 1

the rate Jack paints the house is 1house/4hrs, or 1/4 house/hr.

Jill's rate = 1/6 house/hr

you wanna know what the sum of their rates is. 1/4 house/hr + 1/6 house/hr

To have like terms, let's change to a common denominator & add:

3/12 h/hr + 2/12 h/hr = 5/12 house/hr

So if they paint 5/12 every hr together, then, in 2 hrs, they will have 10/12 done, leaving 2/12 to be painted.

We already know they paint at a rate of 5/12 house per hour. You wanna know how many hrs it takes to paint 2/12 remaining.

2/12 divided 5/12 = ?

Invert & multiply:

2/12 x 12/5 = 2/5 of an hour, or 24 minutes

So it takes 2 hrs & 24 minutes.

Answer 2

Jack can paint a house in 4 hours. So in 1 hour, he can paint 1/4 of the house.
Jill can paint the same house in 6 hours. So in 1 hour, she can paint 1/6 of the house.

So the time they can paint the house together is

1/4 + 1/6= 1/t ( 1 is the whole job)


Convert the two fractions into similar fractions so that we can add them. Find the least common factors of the denominators 4 and 6
Factors of:
4 = 4, 8, 12, 16, 20
6 = 6, 12, 18, 24
12 is the least common factor
1/4 = 3/12
1/6 = 2/12
3/12 + 2/12 = 1/t
Multiply the equation by 12t to remove the denominators
12t( 3/12 + 2/12 = 1/t)
3t + 2t = 12
5t = 12
t = 12/5
t = 2.40 hours ==> the time they will finish the painting job

SIMPLEST SOLUTION
Product/ sum
Product of 4 and 6 => 4 x 6 = 24
Sum of 4 and 6 => 4 + 6 = 10

24/10 = 2.40 hours

Answer 3

Let area to be painted = X units²
In 1 hour Jack paints X/4 units²
In 1 hour Jill paints X/6 units²
Total in 1 hour = X/4 + X/6 = (5/12) X units²
(5/12).X units²<--------> 1 hour
X units²<---------> (X) / ((5/12 ). X) hours
= 12 / 5 hours = 2 h 24 min.

Answer 4

Let
t = time for both to paint the house together

t/4 + t/6 = 1
3t + 2t = 12
5t = 12
t = 12/5 = 2.4 hours = 2 hours, 24 minutes

Answer 5

2 hours 24 min I used the same formula used for parallel resistors ... invert and add the numbers ... so 4 and 6 become 1/4 and 1/6 now convert to a common denominator and you get 3/12 and 2/12 added you get 5/12 reinverting gives 12/5 or 2 and 2/5 or 2.4 which is 2 hours and 24 min ... not taking into account prep or taping or clean up etc

Answer 6

Let the full work =1
4 hour time is taken by Jack to do full part of work i.e. 1
1 hour time is taken by Jack to do the part of work = 1 /4

again,
6 hour time is taken by Jill to do full part of work i.e. 1
1 hour time is taken by Jill to do the part of work = 1 /6

In one hour, both will do =(1/4)+(1/6)
=(6+4)/24
=10/24
=5/12 part
5/12 part is done by both together in 1 hour
1 part is done by both together in 1/(5/12) hour
=12/5 hour
=(2+2/5) hour
=2 hour +(2/5*60)min
=2 hour 24 min. Ans.

Answer 7

I'm not sure and did this all in my head, but I believe it is 12/5 hours, which would be 2 hours and 24 minutes.

Answer 8

2H24M or 2:24

The faster painter will paint 60% of the house. The other, 40%

4*0.6=2.4=2H24M

6*0.4=2.4=2H24M

Answer 9

2 hours, 26 minutes.

Answer 10

assumed one room for each one then after calculate the volume after finish evaluate the time and finally calculate all volume of the house then you can conclusions over all time