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Please help with this maths questions with workings

There are two security guards on a site between 9pm and 7am each night

At 9pm, one of the guards checks the outside of the buildings
This takes him 10 minutes
He repeats this at 10pm and every hour through the night

At 9pm, the other guard checks the inside of each building
This takes him 15 minutes
He repeats this at 10:30pm and every 90 minutes through the night

When the guards are not doing their checks, they are in the security office

Work out how many minutes the security office is empty for during each night
Original post by hbos14
There are two security guards on a site between 9pm and 7am each night

At 9pm, one of the guards checks the outside of the buildings
This takes him 10 minutes
He repeats this at 10pm and every hour through the night

At 9pm, the other guard checks the inside of each building
This takes him 15 minutes
He repeats this at 10:30pm and every 90 minutes through the night

When the guards are not doing their checks, they are in the security office

Work out how many minutes the security office is empty for during each night


It's empty for 40mins. Basically its empty when both checks cross over, this happens at 9pm, 12pm, 3 am and 6 am which is 4 times and the shortest time a security guard is gone is 10mins, 4 lots of 10mins = 40mins.

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