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7-42) Two cities 
X and 
Y are 650 miles apart, Train #1 travels from City 
X to City 
Y at speed of 60 mile/hour. Train #2 travels from City 
Y to City 
X at speed of 70 mile/hour. Train #1 starts at 8:00 am from City 
X and Train #2 starts at 10:00 am from City Y. What time will the two trains meet?

7742-42) Two cities X X and Y Y are 650650 miles apart, Train \#11 travels from City X X to City Y Y at speed of 6060 mile/hour. Train \#22 travels from City Y Y to City X X at speed of 7070 mile/hour. Train \#11 starts at 88:0000 am from City X X and Train \#22 starts at 1010:0000 am from City Y. What time will the two trains meet?

Full solution

Q. 7742-42) Two cities X X and Y Y are 650650 miles apart, Train \#11 travels from City X X to City Y Y at speed of 6060 mile/hour. Train \#22 travels from City Y Y to City X X at speed of 7070 mile/hour. Train \#11 starts at 88:0000 am from City X X and Train \#22 starts at 1010:0000 am from City Y. What time will the two trains meet?
  1. Calculate Train #11 Distance: Calculate the distance Train #11 covers by the time Train #22 starts.\newlineTrain #11 has a 22-hour head start, so distance = speed ×\times time.\newlineDistance = 6060 miles/hour ×\times 22 hours = 120120 miles.
  2. Find Remaining Distance: Subtract the distance covered by Train #11 from the total distance to find the remaining distance.\newlineRemaining distance = 650miles120miles=530miles.650 \, \text{miles} - 120 \, \text{miles} = 530 \, \text{miles}.
  3. Calculate Combined Speed: Calculate the combined speed of the two trains.\newlineCombined speed = speed of Train #11 + speed of Train #22 = 6060 miles/hour + 7070 miles/hour = 130130 miles/hour.
  4. Calculate Meeting Time: Calculate the time it takes for the trains to meet based on the remaining distance and combined speed.\newlineTime = remaining distance / combined speed = 530miles130miles/hour=4.07692307692hours.\frac{530 \, \text{miles}}{130 \, \text{miles/hour}} = 4.07692307692 \, \text{hours}.
  5. Convert Time to Hours and Minutes: Convert the time from hours to hours and minutes.\newline44 hours is 44 hours, and 0.076923076920.07692307692 hours * 6060 minutes/hour =4.61538461538= 4.61538461538 minutes, which is approximately 55 minutes.
  6. Determine Meeting Time: Add the time it takes for the trains to meet to the start time of Train \#22. Train \#22 starts at 10:0010:00 am, so the meeting time is 10:0010:00 am ++ 44 hours and 55 minutes == 2:052:05 pm.