Question

Security A rounds every 2 minutes and 20 seconds in the gate 1. Security B rounds every 1 minute and 40 seconds in the gate 2. If they conduct rounds at the same time. After how many minutes they will rounds together again?

Answer 1

`Time = 11(2)/(3)\ min`

Explanation:

Given

`Security\ A = 2\ mins, 20\ secs`

`Security\ B = 1\ mins, 40\ secs`

Required

After how many minutes, will they round together

First, convert the given time to minutes

`Security\ A = 2\ mins, 20\ secs`

`Security\ A = 2\ mins+ 20\ secs`

`Security\ A = 2\ mins+ (20)/(60)\ min`

`Security\ A = 2\ mins+ (1)/(3)\ min`

`Security\ A = 2(1)/(3)\ min`

`Security\ B = 1\ mins, 40\ secs`

`Security\ B = 1\ mins+ 40\ secs`

`Security\ B = 1\ mins+ (40)/(60)\ min`

`Security\ B = 1(2)/(3)\ min`

So, we have:

`Security\ A = 2(1)/(3)\ min`

`Security\ B = 1(2)/(3)\ min`

List out the multiples of the time of both security personnel take round.

`Security\ A = 2(1)/(3)min,\ 4(2)/(3)min,\ 7min,\ 9(1)/(3)min,\ 11(2)/(3)min...`

`Security\ B = 1(2)/(3)min,\ 3(1)/(3)min,\ 5min,\ 6(2)/(3)min,\ 8(1)/(3)min,\ 10min\ ,11(2)/(3)min,...`

In the above lists, the common time is:

`Time = 11(2)/(3)\ min`

This implies that they go on round after
`11(2)/(3)\ min`