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?

The given rates are in hours per gallon. If we rewrite them in terms of gallons per hour, we have ...

... Jenny + Penny = 1/2 . . . . gallon per hour

... Penny + Lenny = 3/5 . . . gallon per hour

... Jenny + Penny + Lenny = 1 . . . gallon per hour

Subtracting the 2nd equation from the last, we have ...

... (Jenny +Penny +Lenny) -(Penny +Lenny) = (1) -(3/5)

... Jenny = 2/5 . . . . gallon per hour

It will take Jenny 5/2 = 2.5 hours to eat a gallon of ice cream by herself.

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