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 \(1\frac23\) 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?

HelpPLZ Sep 25, 2018

#1**+1 **

Let the portion Jenny can eat in one hour = 1/x

Let the portion that Penny can eat in one hour = 1/y

Let the portion that Lenny can eat in one hour = 1/z

And we have this system

2/x + 2 / y = 1 (1)

(5/3)/y + (5/3)/z = 1 (2)

1/x + 1/y + 1/z = 1 (3)

Multilpy (2) by (3/5) and we have

1/y + 1/z = 3/5 (4)

Put (4) into (3) and we have

1/x + 3/5 = 1 subtract 3/5 from both sides

1/x = 2/5 ⇒ x = 5/2 = 2.5 hrs = time for Jenny to eat the whole gallon by herself

CPhill Sep 25, 2018