I am currently helping a friend's child with his schoolwork. He is currently in primary school and being taught the topic of speed. I would like to give him the following problem as practice but I am not sure how to explain the solution to him at his level:
A and B competed in a race. Every time A ran $7$ m, B ran $3$ m. If B took $14$ minutes to complete the race, how long did A take?
My proposed solution: the ratio of A's speed to B's speed is $7:3$. So A will take a shorter time than B. Since distance $=$ speed $\times$ time, we have distance covered by A $=$ A's speed $\times$ A's time $=$ distance covered by B $=$ B's speed $\times$ B's time, i.e. $7$ $\times$ A's time is equal to $3$ $\times$ B's time. Hence the ratio of A's time to B's time is $3:7$. So, $7u=14,\ 1u=2$ and hence $3u=6$.
How do I rephrase my solution to make it more student-friendly? I am trying not to use any formula.
I think many students have difficulty grappling with the fact that speed is inversely proportional to time. If A's speed is $x$ times B's speed, where $x$ is whole number, then most students can easily see that A's time is $1/x$ times of B's time. But if $x$ is not a whole number, most will get stuck.
I appreciate all advice. Thank you.