SOLUTION: 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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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       Log On


   

Question 651972: 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?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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

           %28matrix%284%2C1%2C%0D%0A%22Josie%27s%22%2C+rate%2C+eating%2C+alone%29%29 + %28matrix%284%2C1%2C%0D%0A%22Cristy%27s%22%2C+rate%2C+eating%2C+alone%29%29 = %28matrix%285%2C1%2C%0D%0Atheir%2C+combined%2Crate%2C+eating%2C+together%29%29   

                   1%2F19 + 1%2F16 = 1%2Fx

Multiply through by 176x to clear of fractions and solve.  You'll
get 176/19 or 9 5/19 minutes.

Edwin