after how many seconds does this happen?

[bumblebee123]

I just can't figure this out!

question: Amy, Bob and Chris are three swimmers. Amy swims the length of a swimming pool in 15 seconds. Bob swims a length of the swimming pool in 20 seconds. Chris swims a length of the swimming pool in 25 seconds. They start at the same end of the swimming pool. they continue swimming until they are all at the same length. After how many seconds does this happen?

I thought the answer would be the LCM of 20,15 and 25 ( 300 ). But the answer is 600.

can anyone help to tell me where I'm going wrong? any help would be really appreciated!

 

[Harry_the_cat]

I just can't figure this out!

question: Amy, Bob and Chris are three swimmers. Amy swims the length of a swimming pool in 15 seconds. Bob swims a length of the swimming pool in 20 seconds. Chris swims a length of the swimming pool in 25 seconds. They start at the same end of the swimming pool. they continue swimming until they are all at the same length. (Should this be "end?) After how many seconds does this happen?

I thought the answer would be the LCM of 20,15 and 25 ( 300 ). But the answer is 600.

can anyone help to tell me where I'm going wrong? any help would be really appreciated!

 

[Dr.Peterson]

Let's check the two answers.

After 300 seconds, Amy has done 300/15 = 20 length s; Bob has done 300/20 = 15 lengths; and Chris has done 300/25 = 12 lengths. At which end is each of them?

Continue.

Then think about what numbers' LCM you should use.

 

[Harry_the_cat]

Yes the answer must be a multiple of 15, 20 and 25. But in this case not the LCM. Here's why:
The LCM is 300 as you said.
But after 300 seconds Amy has swum 300/15 = 20 lengths, Bob has swum 300/20 = 15 lengths, Chris has swum 300/25 = 12 lengths.

Amy and Chris have swum an even number of lengths, but Bob has swum an odd number. So A and C will be back at the end they started at, but B will be at the other end of the pool.

It is therefore important that all three swim an even number of lengths, or all three swim an odd number of lengths.

The next multiple of 15, 20 and 25 is 600. That works!

Edit: Great minds Dr P.

 

[bumblebee123]

Yes the answer must be a multiple of 15, 20 and 25. But in this case not the LCM. Here's why:
The LCM is 300 as you said.
But after 300 seconds Amy has swum 300/15 = 20 lengths, Bob has swum 300/20 = 15 lengths, Chris has swum 300/25 = 12 lengths.

Amy and Chris have swum an even number of lengths, but Bob has swum an odd number. So A and C will be back at the end they started at, but B will be at the other end of the pool.

It is therefore important that all three swim an even number of lengths, or all three swim an odd number of lengths.

The next multiple of 15, 20 and 25 is 600. That works!

Edit: Great minds Dr P.

would i know that it's the next LCM by multiplying 300 by 2?

 

[Steven G]

would i know that it's the next LCM by multiplying 300 by 2?

Please say it is the next CM (common multiple) since the way you say it it seems that you think that there are multiple LCMs
You know that it is the next CM since it brings all swimmers to the same end of the pool and yes the next CM is obtained by multiply the LCM by 2.
You must do an even number of laps to get back to the starting point. If you do an odd number of laps you do not end up at the starting end. But if you double the laps, then all swimmers will have done an even number of laps and hence end up at the same place (the starting point)

If the LCM(a,b,c) is r, the common multiples of a,b and c are simply (integer) multiples of r. Make sure that you see that!