josie can eat a big pizza alone in 22 minutes while cristy can eat a pizza of that size alone in 16 minutes. if one big pizza is to be shared by josie and cristy, how long will it take them to consume the entire pizza?
Without algebra:
The LCM of 22 and 16 is 176. So in 176 minutes Josie will have eaten 8 pizzas
while Cristy will have eaten 11. So together they can eat a total of 19 pizzas
in 176 minutes. Therefore together they can eat 1 pizza in 176/19 or 9 5/19
minutes.
Using algebra. Make this chart:
Pizzas minutes Rate in
eaten required pizzas/mimute
Josie eating alone
Cristy eating alone
Both eating together
Let x be the time for both eating together. Fill that in. Fill in the
given number of minutes required for each eating alone, and fill in 1
for the number of pizzas eaten in all three cases:
Pizzas minutes Rate in
eaten required pizzas/mimute
Josie eating alone 1 22 1/22
Cristy eating alone 1 16 1/16
Both eating together 1 x 1/x
The equation comes from
+ =
+ =
Multiply through by 176x to clear of fractions and solve. You'll
get 176/19 or 9 5/19 minutes.
Edwin