Maths, use a range of multiplicative strategies when operating on whole numbers

This is what we had to do for the extended abstract task. And at the bottom were my answers.



Use a range of multiplicative strategies when operating on whole numbers

 I can apply the strategy to problem solving questions


 


The escape

A prisoner sits in his cell planning his escape. The prisoner is kept in by 5 laser beams, which operate along a corridor. Each laser is switched off at a specific time interval for just long enough to allow a person to walk through. The time between being switched off for each laser is shown below:

Laser One = every 3 minutes
Laser Two = every 2 minutes
Laser Three = every 5 minutes
Laser Four = every 4 minutes
Laser Five = every 1 minutes

The guard patrols and checks the prisoner each time all the laser beams are off simultaneously. Because each laser only switches off for a short time the prisoner knows he can only get past one laser at a time. He has to get past the five lasers from 1 to 5 in order. Laser One is at the entrance of the prisoner’s cell and laser Five is at the door to the outside. He also knows that if he spends longer than 4 minutes 12 seconds in the corridor an alarm will go off.

Can the prisoner escape without the alarm in the corridor going off? Yes

If he can escape, how many minutes should he wait before passing Laser One? 33 minutes

How much time will he have after passing Laser Five before the guard raises the alarm? 12 seconds

I worked it out so if he waits 33 minutes before passing the first laser he will pass it on the 11th laser because it goes off every 3 minutes. Then he will wait 1 minute before passing the next one because it goes off every 2 minutes and that's an even number so he only had to wait 1 minute to pass. Then on the next one it goes off every 4 minutes and so when he goes through the 2nd one he has to wait only 1 more minute and finally on the last one he has to wait 1 minute to go through and then he gets out with 12 seconds to spare.