Problem On Trains

64 Views Asked by At

The distance between two stations $X$ and $Y$ is 220 km.

Trains $P$ and $Q$ leave station $X$ at 7 am and 8:15 am respectively at the speed of 25 km/hr and 20 km/hr respectively for journey towards $Y$.

Train $R$ leaves station $Y$ at 11:30 am at a speed of 30 km/hr for journey towards $X$.

When and where will $P$ be equidistant from $Q$ and $R$ ?

2

There are 2 best solutions below

1
On BEST ANSWER

Let the time of equidistance be $t$ hours after $7$ AM

So, $Q$ will travel $20(t-5/4)=20t-25$ km

$P$ will travel $25t$ km

and $R$ will travel $30(t-9/2)$ km hence is $220- 15(2t-9)=355-30t$ km away from $X$

We need $$20t-25+355-30t=2\cdot25t$$

1
On

Hint: start by analyzing the situation at 11:30