Finding the whole with a tape diagram

We are told that Keisha can run 170 meters in one minute. This is 125 percent of the distance that she could run in one minute three years ago. How far could Kisha run in one minute three years ago?

Pause this video and see if you can figure this out.

All right, now let's do it together. My brain wants to make sure I know the difference between three years ago and today. So today she can run 170 meters in one minute, and what we want to figure out is how much could she run in one minute three years ago.

Well, we know this: 170 meters is 125 of the distance that she could do three years ago. The distance she could do three years ago, of course, is 100 of the distance that she could do three years ago because it's the exact same distance. But I like to think in terms of fractions.

So 125 percent, I could rewrite that as 125 over 100. If I divide both the numerator and the denominator by 25, this is equivalent to 5 over 4.

So that 170 meters, that is five-fourths of what she could do three years ago, and what she could do three years ago would be four-fourths of what she could do three years ago because that's a hundred percent.

And so to figure out if five-fourths is 170 meters, what is four-fourths?

Let us set up a tape diagram right over here, and I'm going to try to hand draw it as best as I can. I want to make five equal sections, and I know it's not exactly, but let's say for the sake of argument for this video, this is five equal sections.

And so if we imagine that each of these are a fourth, this is five-fourths, and then this distance right over here is going to be 170 meters. That's what she could run today.

What we want to do is figure out what is four-fourths. That's the distance that she could run in one minute three years ago. So this is our question mark.

Well, to do that, we just have to figure out how big is each of these fourths. If five of them is 170 meters, well, I just have to divide 5 into 170.

5 goes into 17 three times; 3 times 5 is 15. Subtract, I get a 2 here. Bring down the 0; five goes into 20 four times. Four times five is 20, and it works out perfectly.

So each of these five fourths are 34 meters, 34 meters, 34 meters, 34 meters, 34 meters, and 34 meters.

And so the distance that she could run three years ago is going to be four of these fourths or four of these 34 meters.

So 34 times 4: 4 times 4 is 16. 3 times 4 is 12 plus 1 is 13.

So the mystery distance that she could run in one minute three years ago is 136 meters, and we are done.