We Know

Total work = rate * Time

therefore

30 = Rate * 6

or Rate = \(\frac{30}{6}\) = 5

Now we need to find the number of computers

total work given = 80 and total time = 3 hrs

therefore

80 = 5 * 3 * No. of computers

or No. of computers = \(\frac{80}{15}\) = \(5\frac{1}{3}\), but no. of computers cannot be fraction i.e \(\frac{1}{3}\), so we have to consider as 1.

Total no. of computers = 5+1 = 6.
_________________

We can also just apply some logic...

Given: 1 computer can perform 30 tasks in 6 hours
This means 1 computer can perform 15 tasks in 3 hours (half the time means half the output)
So, 2 computers can perform 30 tasks in 3 hours (Double the number of computers means double the output)
And 3 computers can perform 45 tasks in 3 hours
.
.
.
5 computers can perform 75 tasks in 3 hours
6 computers can perform 90 tasks in 3 hours

Since we can't have a FRACTION as our answer, we need 6 computers to complete the 80 tasks within three hours

Answer:

Cheers,
Brent
_________________

Task performed by one computer in 3 hrs = 15

to perform 80 tasks computers required are 80/15 = 5.33

as the computers cannot be in fraction so answer should be 6

\(\frac{30 tasks}{6 hours} = \frac{5 tasks}{1 hour}\)

Let x = # of machines
So, if we multiply the # of machines by the rate per machine and set that equal to 80/3 we should be able to solve

\(x(\frac{5 tasks}{hour})= \frac{80 tasks}{3 hours}\)

solve for x

\(x = \frac{80 tasks}{3 hours}*\frac{1 hour}{5 tasks}\)

\(x = \frac{80}{15} = 5\frac{5}{15} = 5\frac{1}{3}\)

So, we need at least 5 and 1/3 machines, and since machines don't come in less than whole numbers, we need 6 machines.

PS I mean "computers" not "machines"

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