Question

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?

Answer 1

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.