I need help with this alegrab questions please!?

Question

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?

These are the answers that I've been given:
2 hours and 24 minutes
3 hours and 12 minutes
3 hours and 44 minutes
4 hours and 10 minutes
4 hours and 33 minutes

Now, I know that the correct answer is 2hours and 24minutes but I don't know HOW to get the answer... if there are any math geniuses out there, PLEASE HELP ME!!!

oopps... i meant ALGEBRA

Answer 1

The part about Sally being able to paint the house in 4 hours implies that she paints at a rate of 1 house per 4 hours, or 1/4 [houses/hr]. For John, that would be 1/6 [houses/hr]. When they paint together, their combined rate is:

1/4 + 1/6 [houses/hr]

The question for the duration to complete the painting of one house can be represented as:

(Number of painted houses) = (Painting duration) * (Painting rate)

...and applying the known information, the problem to solve becomes:

1 [house] = time [hours] * (1/4 + 1/6 [houses/hr])
12 = time * (3 + 2)
time = 12/5 = 2 2/5 [hrs] = 2 hr and 24 min

Answer 2

Sally paints at 1/4 house per hour.
John paints at 1/6 house per hour.

Since they will be both painting for the same time (as they will be both finished when the house is completely painted), we have

X * (1/4 + 1/6) = 1

Where X is the time, and 1 is the number of houses.

A bit of algebra (we turn the fractions into a common denominator)

X * (3/12 + 2/12) = 1

X * (5/12) = 1

and we multiply both sides by 12/5, so X becomes isolated

X = 12/5

But look here, X is our answer, in hours.

12/5 is 2 hours and 2/5, and 2/5 of an hour is 24 minutes.

Answer is 2 hours 24 minutes.

Algebra is not difficult, it does not require genius. The real trick is to turn the question into the right equations. Don't be afraid, it is a lot simpler than you think, you just have to try.

Answer 3

x/4 + x/6 = 1
x represents time

Multiply both sides of the equation by the LCD which is 12 and you get 3x + 2x = 12.........5x = 12.......x = 2 2/5 which is 2 hours and 24 minutes

Answer 4

let A be the area of the house
let t denote time

t1 = A/R1 = 4
t2 = A/R2 = 6
where R1 is the rate for Sally
and R2 is the rate for John

therefore
A = 4*R1
A = 6*R2
6*R2 = 4*R1
R2 = 4/6*R1

tboth = A/(R1+R2)
= 4*R1/(R1+4/6*R1)
cancel the R1s
= 4/(1+2/3)
=2.4
= 2hours 24 minutes

QED

Answer 5

try working out the percentage of the house that each person covers in a set time, say 1 hour :p

Answer 6

6 Hours, because Sally will just sit around tell John where he missed.

Answer 7

2 h & 24 min