If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? .......how do you figure out the answer to this question?
2007-01-18 08:00:04 · 18 answers · asked by ducks rock 1 in Science & Mathematics ➔ Mathematics
Think this through...
Sally paints at a rate of 1/4 of a house per hour, or t/4.
John paints at a rate of 1/6 of a house per hour, or t/6.
Now, each of them will paint for the same amount of time; t is the same in both formulas.
Since they paint at different rates, they will paint different amounts of the house, but the amounts that they paint will add to 1 (the whole house has been painted once they are done).
So, we have the following formula:
1 = t/4 + t/6
This means Sally has painted t/4 and John has painted t/6, and together, they have painted 1 house. Now find t and you have the answer:
24 = 6t + 4t
t = 24/10 = 2.4 hours
2007-01-18 08:05:57 · answer #1 · answered by computerguy103 6 · 2⤊ 0⤋
Sally paints 1/4 of the house every hour, and John paints 1/6 of the house every hour.
Set up the question as thus:
1/4 + 1/6 = 1/x
Solve for X.
X/4 + X/6 = 1
which simplifies to
5X/12 = 1
and multiplying by the reciprocal,
X= 12/5, or 2.4 hours.
2007-01-18 08:10:26 · answer #2 · answered by πρ 6 · 0⤊ 0⤋
Sally does in 1 hour 1/4
John does in 1 hour 1/6
Sally and John do in 1 hour = 1/4 + 1/6 = 3/12 + 2/12 = 5/12
Both can do the work in 1 /(5/12)= 1 x 12/5 = 2.4 days (2 2/5 days)
2007-01-18 08:07:18 · answer #3 · answered by Sheen 4 · 1⤊ 1⤋
Look at it from another angle...Sally can paint 1/4 of a house in an hour, John 1/6. So together they can paint 5/12 of a house in an hour, which means they'll be done in 2.4 hours.
The general form for these types of problems is (x + y)/(x * y).
2007-01-18 08:04:48 · answer #4 · answered by Jim C 4 · 1⤊ 0⤋
Sally - 4 hours
John - 6 hours
Total man hours = 10
Average time = 5 hours
2 people, so 2.5 hours to both paint house.
2007-01-18 08:04:00 · answer #5 · answered by Anonymous · 2⤊ 1⤋
x / 4 + x / 6 = 1
The common denominator is 12.Multiply the equation by 12.
12(x/4) + 12(x / 6) = 12(1)
3x + 2x = 12
5x = 12
5x / 5 = 12 / 5
x = 2 2/5
x = 2.4 hours. . .. .4 is the percent of a hour. 4 x 60 = 24
x = 2 Hours 24 minutes
x = 2' 24"
Sally and John can complete the painting in 2 hours and 24 minutes
- - - - - - - - -s-
2007-01-18 08:22:56 · answer #6 · answered by SAMUEL D 7 · 0⤊ 0⤋
4 hours = 1/4 work rate...
6 hours = 1/6 work rate...
Rate for Sally is 1/4
Rate for John is 1/6
That is... in 1 hour Sally complete's 1/4 of the job. In 2 hours she completes 2/4 or 1/2 of the job. In 3 she completes 3/4 of the job. And in 4 hours she complete's 4/4 or 1 of the job.
Time working together is x
For Sally it is x
For John it is x
Fractional part of the job done for Sally is 1/4x
Fractional part of the job done for John is 1/6x
1/4x + 1/6x = 1
The LCD is 12
12(1/4x) + 12(1/6x) = 12(1)
3x + 2x = 12
5x = 12
divide both sides by 5
x = 12/5
x=2.4
2007-01-18 08:14:19 · answer #7 · answered by Anonymous · 0⤊ 0⤋
Its 2.4 Hours. 2 Hours and 24 mins
Time of Each person Multiplied / Sum of Each person
(4 * 6) / (4 +6)
24 /10
2.4 Hours
Why would it take LONGER than 4 hours if it takes just one of them 4 hours to paint it.
2007-01-18 08:06:46 · answer #8 · answered by Vic 2 · 0⤊ 0⤋
We assume 1. Sally and John will paint at the same time and will continue until it is finished. 2.assume the house is 1000 square feet.
Sally paints at the rate of 250 square feet per hour and John Paints at the rate of 166.67 feet per hour
S=1000/4=250
J=1000/6=166.67
T=250+166.67=416.67 square feet per hour
1000/416.67=2.4hours=2hours 24minutes
2007-01-18 08:31:56 · answer #9 · answered by heyyou 1 · 0⤊ 0⤋
it takes 4 hr. for sally and 6 hr. for john
john takes 1.5 times as long as sally
if they work together sally paints 63% of the house and john paints the rest. in total it takes 2.4 hr.
63% of 4 is 2.4
2007-01-18 08:11:18 · answer #10 · answered by trevelan7 2 · 0⤊ 0⤋