Two tractors $T_1$ and $T_2$ start at the same moment towards each other from two farm stations $P$ and $Q$ separated by $180\text{ km}$. Tractor $T_1$ travels at $24\text{ km/h}$ and $T_2$ travels at $36\text{ km/h}$. The distance in kilometres from station $P$ where the two tractors meet is ________ (answer in integer).
Answer Key:
72
Step-by-Step Solution & Explanation
1. Relative speed of approaching tractors:
$v_{\text{rel}} = v_1 + v_2 = 24 + 36 = 60\text{ km/h}$
2. Time elapsed until meeting:
$t = \frac{D}{v_{\text{rel}}} = \frac{180}{60} = 3\text{ hours}$
3. Distance traversed by $T_1$ from station $P$:
$D_P = v_1 \times t = 24 \times 3 = 72\text{ km}$