Elementary School Question on a race between a frog and a rabbit.

Question

In a race, a frog tried to catch up with a rabbit which started 162m ahead of the frog. For every 3.8m jump that the frog made, the rabbit made a 0.8m jump at the same time. How many jumps would the frog have to make in order to catch up with the rabbit? I understand the way of solving this question would be,

$3.8-0.8=3$

To find the difference, after that, to find the amount of steps:

$162 ÷ 3 = 54 steps$

But I do not know how to explain my workings. My question is that how should I explain my workings to my younger brother so that he understands?

Answer 1

First, show him a couple of steps. Explain how

• After one jump, the rabit travelled $0.8$ while the frog travelled $3.8$
• After two jumps, the rabit travelled $1.6$ while the frog travelled $7.6$ so the difference is now $6$
• After $3$ jumps, the difference is $9$.

Now, we can see a pattern. We can see that after each jump, the difference between the two decreases by $3$.

So, now we simply need to know the answer to the question

How many times must the difference decrease by $3$ untill it will be $0$?

which, in other words, is the quesiton $3$ times what is $162$, and the answer is $162:3$.

Answer 2

I would start with the rabbit 3m ahead and ask how many jumps.

Then 6m ahead.

Then 30m ahead.

If your younger brother understands division, ask if he notices a pattern.

Then ask about 162.

If he seems to get all this, ask about non-multiples of 3 uch as 2, 4, and 10.