Sliding Question

Question

At the local playground, three boys like to go down the a very wide slide. After going down the slide, they turn around and climb back up the slide rather than walking around to climb the ladder. The slide is so wide that they can all slide and climb at once without crashing into each other. Each boy slides down the slide in two seconds. It takes Kasey 5 seconds to climb back up. It takes Zack 6 seconds to climb back up. It takes Denny seven seconds to climb back up the slide. They all start together at the same time and slide down. How many seconds after starting will they all slide down together at the same time again?

I started trying to work this problem and am confused on how I will get the answer.

On the first slide down It takes everyone 2 seconds so it is 1st: k=2 z=2 d=2

On the second slide down it will take kasey 5 seconds to go up and 2 sec. to come back down so it will look like: k=9 z=10 d=11

On the third slide down: k=16 z=18 d=20

Each time it will increase by a number leaving me confused on how to find when they will all slide down again at the same time if each time it is going to increase. Have I set up the problem right?

Answer 1

Hint: $lcm(7,8,9)=504~~~~~~~~$

Answer 2

Each child gets to the top at regular intervals, so the time elapsed since the start would be a multiple of the interval length. For example Kasey gets to the top at every multiple of 7 seconds. Since they all start sliding down at the same time, we just need to find out the smallest period of time that is a multiple of the interval lengths of all three children. That is called the lowest common multiple, or LCM for short.