SOLUTION: If it takes Sally 4 hours to paint a house and John 6 hours to paint the same house, how long does it take them to paint the house together?

Question 200990: If it takes Sally 4 hours to paint a house and John 6 hours to paint the same house, how long does it take them to paint the house together?
Found 2 solutions by stanbon, RAY100:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If it takes Sally 4 hours to paint a house and John 6 hours to paint the same house, how long does it take them to paint the house together?
--------------------------
Sally DATA:
time = 4 hrs/job ; rate = 1/4 job/hr
---------------------
John DATA:
time = 6 hrs/job ; rate = 1/6 job/hr
-------------------------
Together DATA:
time = x hrs/job ; rate = 1/x job/hr
=========================================
Equation:
rate + rate = together rate
1/4 + 1/6 = 1/x
3x + 2x = 12
5x = 12
x = 12/5 = 2 2/5 hrs
x = 2 hrs and 24 minutes
==============================================
Cheers,
Stan H.
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Rate of Sally = 1 house / 4 hrs = .25 House / hr
.
Rate of John = 1 house / 6 hrs = .167 house / hr
.
combined rate is .417 house per hr,,,,(.25 +.167)
.
Rate * Time = Distance
.
.417 house / hr * t hrs = 1 house
.
t= 1 / .417 = 2.4 hrs
.
check
.
2.4 * 1/4 + 2.4 * 1/6 = .6+.4 =1,,,,,, ok

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