A11:25 AM
B9:38 PM
C10:34 AM
D1:11 PM
Answer:
A. 11:25 AM
Read Explanation:
Calculate Travel Time for Each Train:
Train A: Departs at 7:20 AM, Arrives at 2:20 PM. Total travel time = 7 hours.
Train B: Departs at 9:20 AM, Arrives at 2:20 PM. Total travel time = 5 hours.
Assume a Standard Distance: To simplify calculations, let's assume the distance between station M and station N is a convenient number that is a multiple of the travel times (7 and 5 hours). The least common multiple (LCM) of 7 and 5 is 35. So, let the distance be 350 km (a multiple of 35 for easier division).
Calculate Individual Speeds:
Speed of Train A = Distance / Time = 350 km / 7 hours = 50 km/hr.
Speed of Train B = Distance / Time = 350 km / 5 hours = 70 km/hr.
Determine the Head Start of Train A:
Train B starts at 9:20 AM, while Train A starts at 7:20 AM.
Train A travels for 2 hours (from 7:20 AM to 9:20 AM) before Train B starts.
Distance covered by Train A in these 2 hours = Speed × Time = 50 km/hr \times 2 hours = 100 km.
Calculate Remaining Distance and Relative Speed:
When Train B starts (at 9:20 AM), the remaining distance between the trains is 350 km - 100 km = 250 km.
Since the trains are moving towards each other, their relative speed is the sum of their speeds: 50 km/hr + 70 km/hr = 120 km/hr.
Calculate Time to Meet:
The time it takes for them to meet after Train B starts is: Time = Remaining Distance / Relative Speed.
Time = 250 km / 120 km/hr = 25/12 hours.
Convert Time to Hours and Minutes and Add to Starting Time:
25/12 hours = 2 hours and 1/12 of an hour.
1/12 of an hour = (1/12) × 60 minutes = 5 minutes.
So, they meet 2 hours and 5 minutes after Train B starts (which is 9:20 AM).
Meeting Time = 9:20 AM + 2 hours 5 minutes = 11:25 AM.