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 = $\tt\frac{1}{2.75}$

Amount of work done in x days = $\tt\frac{x}{2.75}$

Amount of work done by Computer B⤵️

Amount of work done in one day = $\tt\frac{1}{3.5}$

Amount of work done in x days = $\tt\frac{x}{3.5}$

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

$\sf \: \frac{x}{2.75} + \frac{x}{3.5} = 1$

Solve for x ~

$\sf \frac{x}{ \frac{11}{4} } + \frac{x}{ \frac{7}{2} } = 1$

$\sf \frac{4x}{11} + \frac{2x}{7} = 1$

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

$\sf \: 50x = 77$

$\sf \: x = \frac{77}{50}$

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

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