Algebra word problem

Question

A large concrete mixing machine can mix a certain amount of concrete in 12 hours, while a smaller one can mix the same amount in 20 hours. Mixing simultaneously, how long would it take both machines to mix the same amount of concrete?

Answer 1

One does the job in 12 hours.  The other does the job in 20 hours.

We need to find out how much each does in one hour, add that amount

and then solve for the number of hours that total would be multiplied

by to do the whole job or 100%

 

Note that the final answer should be less than 12 hours.

 

Machine 1 does 1/12 of the job per hour

Machine 2 does 1/20 of the job per hour

 

(1/12 + 1/20)(x hours) = 1

The lowest common multiple of 12 and 20 is 60 so let's change

our fractions to 60ths..

 

[(1/12)(5/5) + (1/20)(3/3)](x hours) = 1

(5/60 + 3/60)x = 1

(8/60)x = 1    we can reduce 8/60 by dividing out a 4

(2/15)x = 1    multiply both sides by 15/2

x = 15/2

x = 7 1/2  or 7.5 hours

 

this answer makes sense because working together the total time

to complete the job must be less than either machine working alone.