The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time will they meet?
10.30 a.m.
10 a.m.
12 a.m.
11 a.m.
Explanation:
Assume that they meet x hours after 8 a.m.
Then, train 1, starting from A, travels x hours till the trains meet.
Distance travelled by train 1 in x hours =60x km
Train 2, starting from B, travels (x−1) hours till the trains meet.
Distance travelled by train 2 in (x−1) hours =75(x−1) km
Total distance travelled
= Distance travelled by train 1 + Distance travelled by train 2
⇒330=60x+75(x−1)
⇒12x+15(x−1)=66
⇒12x+15x−15=66
⇒27x=66+15=81
⇒3x=9
⇒x=3
Hence, the trains meet 3 hours after 8 a.m., i.e. at 11 a.m.
Assume that they meet x hours after 8 a.m.
Then, train 1, starting from A, travels x hours till the trains meet.
Distance travelled by train 1 in x hours =60x km
Train 2, starting from B, travels (x−1) hours till the trains meet.
Distance travelled by train 2 in (x−1) hours =75(x−1) km
Total distance travelled
= Distance travelled by train 1 + Distance travelled by train 2
⇒330=60x+75(x−1)
⇒12x+15(x−1)=66
⇒12x+15x−15=66
⇒27x=66+15=81
⇒3x=9
⇒x=3
Hence, the trains meet 3 hours after 8 a.m., i.e. at 11 a.m.