Question

A man starts running from point $P$ at $11:00a.m$ with a speed of $10km/hr$. He runs for $2$ hours and then takes a $1$ hour rest. He continues this till e is caught by another man who starts at $2:00p.m$ from point $P$ and runs non-stop at a speed of $15km/hr$ towards the first man. At what time (in $p.m$) will the first man be caught?

Answer 1

Speed of light man $=10km/hr$

The man runs for 2 hours and then takes a 1 hour rest.

Distanced covered by him in $3$ hrs $=2\times 10=20km$

Speed of second man $=15km/hr$

Now, at $2.00pm$, the second man starts running and the first man is at a distance of $20km$. After $2$ hours , at $4:00pm$, distance covered by first man $=20km$ and he will not move for another hour.

and distance covered by second man $=2\times 15=30km$

$\Rightarrow$ Distance b\w them at $4:00pm=30-20=10kjm$

Now,

Time taken to cover $10km$ by second man

$=\frac{10}{15}=\frac{2}{3}hours$

$(\frac{2}{3}\times 60)minute=40$ minutes

Total time taken to catch first man from $2:00pm=2hr$ and $40$minutes.

$\therefore$ At $4:40$ pm the first man will be caught