Anonymous

# If Sally can paint a house in 4 hours, and John 6?

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?

A. 2 hours and 24 minutes

B. 3 hours and 12 minutes

C. 3 hours and 44 minutes

D. 4 hours and 10 minutes

E. 4 hours and 33 minutes

PS show me the steps...thanks

Relevance

Do these as rates:

Sally can paint 1/4 of the house per hour

John can paint 1/6 of the house per hour

Working together for T hours, they will complete the whole house.

(1/4 + 1/6)T = 1

Get a common denominator of 12:

(3/12 + 2/12)T = 1

(5/12)T = 1

T = 12/5

T = 2 2/5 hours

T = 2 hours 24 minutes

P.S. The shortcut to these rate problems is:

AB / (A + B)

A = 4

B = 6

4*6 / (4 + 6)

= 24/10

= 2.4 hours

(Remember 0.4 x 60 = 24 minutes)

A. 2 hours 24 minutes

• Anonymous

sally paints 1/4 of the house in 1 hour, because in four the whole house is done.

for the same reason, john paints 1/6 in 1 hour.

1/4 we have to change to 3/12

and 1/6 to 2/12

now thats 5/12 for 1 hour with both of them.

so it would be 10/12 for 2 hours.

then 2/12 left.

and don't figure it out, just choose A because it's the only one that is 2 hours. sorry. I'm only 11.