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 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 1

J, P, and L can each eat ice cream at respective rates of
`\frac1j,\frac1p,\frac1\ell` in gallons of ice cream per hour (gal/hr).

We're given that

`\frac1j+\frac1p=\frac12`

`\frac1p+\frac1\ell=\frac13`

`\frac1j+\frac1p+\frac1\ell=1`

We want to find
`\frac1j`. Subtracting the second equation from the third gives

`\left(\frac1j+\frac1p+\frac1\ell\right)-\left(\frac1p+\frac1\ell\right)=1-\frac13`

`\implies\frac1j=\frac23`

so J can eat 2 gallons of ice cream in 3 hours, or 2/3 of a gallon per hour, so that it would take her 3/2 hours, or 1.5 hours, to eat 1 gallon on her own.