Question

Two computers just scanned for viruses at the same time. Computer A runs a virus scan every 2.75 days. Computer B runs a virus scan every 3.5 days. How long will it be until both computers run a virus scan at the same time again?

(please help it's like 1 AM rn and I have an overdue assignment)

Answer 1

Let the time taken by computer for virus scan be, 'x' days

We are given that Computer A runs a virus scan in every 2.75 days and Computer B runs a virus scan in every 3.5 days.

Amount of work done by computer A⤵️

Amount of work done in one day =
`\tt(1)/(2.75)`

Amount of work done in x days =
`\tt(x)/(2.75)`

Amount of work done by Computer B⤵️

Amount of work done in one day =
`\tt(1)/(3.5)`

Amount of work done in x days =
`\tt(x)/(3.5)`

Since, They are doing the same work the amount of work done is 1.

`\sf \: (x)/(2.75) + (x)/(3.5) = 1`

Solve for x ~

`\sf (x)/( (11)/(4) ) + (x)/( (7)/(2) ) = 1`

`\sf (4x)/(11) + (2x)/(7) = 1`

`\sf \: 28x + 22x = 77`

`\sf \: 50x = 77`

`\sf \: x = (77)/(50)`

`\boxed{ \bf \: x = 1.54}`

➪ Thus, the time taken when both computers run a virus scan at the same time again is, 1.54 days