Problema Solution
Ron can make a batch of 100 large pizza crusts in 1.2h less than Chad. Together they can do the job in 1.8h. How long does it take each to do the job alone?
Answer provided by our tutors
let
r = the time that Ron needs to make a batch of 100 pizza crusts, thus his rate is 100/r pizzas per hour, r>0
c = the time that Chad needs to make a batch of 100 pizza crusts, thus his rate is 100/c pizzas per hour, c>0
Ron can make a batch of 100 large pizza crusts in 1.2 h less than Chad
r = c - 1.2
Together they can do the job in 1.8 h:
100/r + 100/c = 100/1.8
plug r = c - 1.2 into the last equations
100/(c - 1.2) + 100/c = 100/1.8
by solving we find
c1 = 4.3 hr
c2 = 0.5 hr
click here to see the step by step solution of the equation
since r>= 0 then c - 1.2 >0 or c>1.2
we conclude that c = 4.3 hr and r = 4.3 - 1.2 = 3.1 hr
Ron needs 3.1 hours to make a batch of 100 large pizza crusts.
Chad needs 4.3 hours to make a batch of 100 large pizza crusts.