Superman goes around the world in $2.5$ hrs, and Flash in $1.5$ hrs. How many times will they pass each other going in opposite directions in 24 hrs? Superman and Flash are running around the world in opposite directions. Superman can go around the world in $2.5$ hours, and Flash can do the same in $1.5$ hours. Assuming they start at the same time and place, how many times will they pass each other going in opposite directions in a $24$-hour period?
Superman in 24 hours
$\frac{24}{2.5}=9.6$ laps around the world
Flash in 24 hours
$\frac{24}{1.5}=16$ laps around the world
Superman in an hour
$\frac{9.6}{24}=0.4$ laps around the world
Flash in an hour
$\frac{16}{1.5}=0.\dot{6}$ laps around the world
So in an hour Flash passes Superman at over half of his lap. Their combined lap length is $> 1$.
This much I've understood but couldn't go further myself. However, I found a solution that gave me an answer and partially helped my understanding but I still can't reason why the answer makes sense.

Let the circumference of the Earth $= C$.
Every hour Superman covers $\frac{C}{2.5} = \frac{C}{5/2}=\frac{2}{5}C$
And every hour Falsh covers $\frac{C}{1.5}= \frac{C}{3/2}=\frac{2}{3}C$
So every hour they cover $(\frac{2}{5} + \frac{2}{3})C = \frac{16}{15}C$
Which means that it takes them $\frac{15}{16}$ hrs to meet every time.
So the number of times they meet in $24$ hrs = $\frac{24}{15/16} = 25.6 \approx 25$ times.

The number of times they meet is just the sum of the number of laps both Superman and Flash go around the world in $24$ hrs $16 + 9.6$.
Unfortunately (and embarrassingly), I can't see why. Please help with clarifications.
 A: Since they run in opposite directions, from Superman's point of view, he's not moving and the Flash is running around the Earth at the speed $(1/2.5 + 1/1.5)$ laps /hr $= 16/15$ laps /hr. Multiplying this by the number of hours means Flash passes him $25.6$ times.
A: They meet when their lap length is $1$. Since they start at the same time, let $t$ be the time passed till they meet. So,
$$\frac{\text{Earth}}{2.5 h}t + \frac{\text{Earth}}{1.5 h}t = \text{Earth}$$ Solving this you get
$$\frac {4 \times \text{Earth}}{3.75 h}t = \text{Earth}$$ Solving, you get $t = 0.9375$ and $0.9375$ = $\frac{15}{16}$. Now, just divide $24$ by $\frac{15}{16}$ and you get $\frac{24 \times 16}{15}$ which is roughly $25.6$ and $25.6$ ~ $25$. So they meet $25$ times in an hour
A: Here is one way to look at it -
For them to complete one lap together, the time taken is
$t = \displaystyle \frac{2.5 \times 1.5}{4} = 0.9375 \ hr \tag1\ $
To derive $(1)$,
Speed of Flash $s_a = \frac{1}{1.5}$ lap / hr.
Speed of Superman $s_b = \frac{1}{2.5}$ lap / hr.
It is easy to see equation $(1)$ using relative speed. As they are traveling in opposite direction, to complete $1$ lap together, it will take them $\displaystyle \frac{1}{s_a + s_b}$ hr.
You can also derive equation $(1)$ as below -
When they meet first time, if Flash has traveled $x$, Superman has traveled $(1-x)$ in the same amount of time $t$.
$\displaystyle t = \frac{x}{s_a} = \frac{1-x}{s_b}$ and you can solve to get equation $(1)$.
Now for them to meet next, they again need to complete one lap together. So  number of times they meet in $24$ hour is given by,
$ \displaystyle n = \lfloor \frac{24}{0.9375} \rfloor = 25$
