Two trains A and B start at the same time from P and Q respectively and move towards each other. After they cross each other, trains A and B take 9 hours and 16 hours respectively to reach their destinations. If the speed of train A is 40 km/hr, what is the distance between P and Q?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 840 km
If two trains meet and then take \(t_{1}\) and \(t_{2}\) hours to finish, their speeds are in the ratio \(\sqrt{t_{2}}:\sqrt{t_{1}}\). After the meeting, each train covers the part that the other train covered before it.
Speed of A : speed of B \(=\sqrt{16}:\sqrt{9}=4:3\)
Speed of B \(\displaystyle =40\times\frac{3}{4}=30\) km/hr
After the meeting, A covers B’s part: \(40\times9=360\) km
B took \(\displaystyle \frac{360}{30}=12\) hr to cover that part, so they met after 12 hr
Distance PQ \(=(40+30)\times12=70\times12=840\) km