+1310 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 2/3 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?
For a question like this, it is essential that you explain carefully to your reader what any variable that you introduce represents.
+128731 Call the amoiunt Jenny can eat in one hr, x, the amount Penny can eat in one hour, y and the amount Lenny can eat in one hour = z.....so we have
1x +1 y + 1z = 1
2x + 2y = 1 → 2y = 1 - 2x → y = [1 -2x] / 2 (a)
(5/3)x + (5/3)z = 1 → (5/3)z = 1 - (5/3)x → z = (3/5) - x (b)
And substituting (a) and (b) into the first equation, we have
1x + [1 -2x] /2 + (3/5) - x = 1 simplify
{1 - 2x] / 2 + (3/5) = 1 subtract 3/5 from both sides
[1 - 2x] / 2 = 2/5 multiply both sides by 2
1 - 2x = 4/5
2x = 1 - 4/5
2x = 1/5 divide by 2 on both sides
x = 1/10 [of a gallon] this is the amount that Jenny eats in one hour
So...just invert this...and it takes Jenny 10 hrs. to eat one gallon by herself......she's a pretty slow eater!!!!
+128731 Call the amoiunt Jenny can eat in one hr, x, the amount Penny can eat in one hour, y and the amount Lenny can eat in one hour = z.....so we have
1x +1 y + 1z = 1
2x + 2y = 1 → 2y = 1 - 2x → y = [1 -2x] / 2 (a)
(5/3)x + (5/3)z = 1 → (5/3)z = 1 - (5/3)x → z = (3/5) - x (b)
And substituting (a) and (b) into the first equation, we have
1x + [1 -2x] /2 + (3/5) - x = 1 simplify
{1 - 2x] / 2 + (3/5) = 1 subtract 3/5 from both sides
[1 - 2x] / 2 = 2/5 multiply both sides by 2
1 - 2x = 4/5
2x = 1 - 4/5
2x = 1/5 divide by 2 on both sides
x = 1/10 [of a gallon] this is the amount that Jenny eats in one hour
So...just invert this...and it takes Jenny 10 hrs. to eat one gallon by herself......she's a pretty slow eater!!!!
