SOLUTION: One machine took 90 minutes while another took 40 minutes to produce the same number of similar can drinks. The faster machine produced 40 more can drinks per minute than the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One machine took 90 minutes while another took 40 minutes to produce the same number of similar can drinks. The faster machine produced 40 more can drinks per minute than the      Log On


   

Question 1031791: One machine took 90 minutes while another took 40 minutes
to produce the same number of similar can drinks.
The faster machine produced 40 more can drinks per minute
than the slower one.
If both machines were switched on at the same time, what
was the total number of can drinks produced after 6 hours.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
One machine took 90 minutes while another took 40 minutes
to produce the same number of similar can drinks.
The drink-making rate of the first machine is x drinks per 
90 minutes or %28x_drinks%29%2F%2890_minutes%29 or x%2F90drinks%2Fminute.

The drink-making rate of the second machine is x drinks per 
40 minutes or %28x_drinks%29%2F%2840_minutes%29 or x%2F40drinks%2Fminute.

The faster machine produced 40 more can drinks per minute
than the slower one.
x%2F40drinks%2Fminute%22%22=%22%22x%2F90drinks%2Fminute%22%22%2B%22%2240%28drinks%29%2F%28minute%29%7D%7D%0D%0A%0D%0A%7B%7B%7Bx%2F40=x%2F90%2B40

Multiply both sides by LCD = 360
 
9x=4x%2B14400

5x=14400

x=2880

So the slower machine's drink-making rate is

x%2F90drinks%2Fminute =
2880%2F90drinks%2Fminute =
32drinks%2Fminute

And the faster machine's drink-making rate is

x%2F40drinks%2Fminute =
2880%2F40drinks%2Fminute =
72drinks%2Fminute

If both machines were switched on at the same time,
what was the total number of can drinks produced after 6 hours
6 hours is 6*60 or 360 minutes.

In 360 minutes the slower machine will produce 32*360 or 11520 drinks.
In 360 minutes the faster machine will produce 72*360 or 25920 drinks.

11520 drinks + 25920 drinks = 37440 drinks.

Edwin