+144 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?
+128474 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
