SOLUTION: Jenny and Penny can eat a whole gallon of ice cream together in 2 hours. Penny and Lenny can eat a whole gallon of ice cream together in 1 2/3 hours. All three together can eat a w
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Question 964529: Jenny and Penny can eat a whole gallon of ice cream together in 2 hours. Penny and Lenny can eat a whole gallon of ice cream together in 1 2/3 hours. All three together can eat a whole gallon of ice cream together in 1 hour. How many hours would it take Jenny to eat a whole gallon of ice cream all by herself?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Jenny and Penny can eat a whole gallon of ice cream together in 2 hours. Penny and Lenny can eat a whole gallon of ice cream together in 1 2/3 hours. All three together can eat a whole gallon of ice cream together in 1 hour. How many hours would it take Jenny to eat a whole gallon of ice cream all by herself?
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Use a set of equations of rates to get:
j + p = 1/2 job/hr
p + L = 3/5 job/hr
j + p + L = 1/1 job/hr
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Substitute for "j" and for "L" and solve for "p"::
(1/2)-p + p + (3/5)-p = 1
Simplify::
(1/2)+(3/5) - p = 1
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(5+6)/10 - p = 1
-p = -1/10
p = 1/10 (Penny's rate)
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Solve for "J"
j + p = 1/2
j + 1/10 = 1/2
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j = (5/10) - (1/10)
j = 4/10 = 2/5 (Jenny's rate)
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Ans:: Jenny's time to do the job alone:: 5/2 = 2 1/2 hrs
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Cheers,
Stan H.
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