Two trains A and B start at the same time from stations X and Y respectively and move towards each other. After they cross each other, trains A and B take 49 hours and 36 hours respectively to reach their destinations. If the speed of train A is 36 km/hr, what is the distance between X and Y?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 3276 km
The part A covers before the crossing is the part B covers after it, and the other way round. Writing both gives the speed ratio and the time to the crossing.
Let the trains cross after \(t\) hours, with speeds \(a=36\) and \(b\) km/hr
Distance from X to the crossing: \(at=36b\); distance from Y to the crossing: \(bt=49a\)
Dividing: \(\displaystyle \frac{a}{b}=\frac{36b}{49a}\), so \(\displaystyle \frac{a^{2}}{b^{2}}=\frac{36}{49}\) and \(\displaystyle \frac{a}{b}=\frac{6}{7}\)
Speed of B \(\displaystyle =36\times\frac{7}{6}=42\) km/hr
\(\displaystyle t=\frac{49a}{b}=49\times\frac{6}{7}=42\) hours
Distance XY \(=(36+42)\times42=78\times42=3276\) km
The distance between X and Y is 3276 km.