At 9.30 a.m., a car left town X for town Y at a speed of 60km/h for the whole journey. At 11 a.m., a lorry started from town Y and travelled towards town X. The speed of the lorry remained the same until it passed the car at 12.30 p.m. The lorry passed the car at midpoint between X and town Y and decreased its speed by 20km/h. It travelled at the new speed for the rest of the journey. What time did the lorry reach town X?
The car traveled for 3 hours, meaning that the distance from X to Y is 360 km.
The lorry covered its 180 km in 1.5 hours, meaning it was going 120 km/hr.
Then the lorry proceeded at 70 km/hr, needing 180/70 = 2 4/7 hours to cover the remaining 180 km.
2 4/7 hrs = 2 hrs 34 min.
So, the lorry reached X at 3:04 pm
To find out what time the lorry reached town X, we need to calculate the time it took for the lorry to travel from the midpoint between town X and town Y to town X.
Let's break down the information given:
1. The car left town X at 9:30 a.m. and traveled at a speed of 60 km/h for the entire journey.
2. The lorry started from town Y at 11:00 a.m.
3. The lorry passed the car at the midpoint between town X and town Y at 12:30 p.m. This means the lorry took 1.5 hours (12:30 p.m. - 11:00 a.m.) to reach the midpoint.
4. At the midpoint, the lorry decreased its speed by 20 km/h.
To calculate the time it took for the lorry to reach town X from the midpoint, we need to know the distance between the midpoint and town X, as well as the new speed of the lorry.
Let's assume the distance between the midpoint and town X is 'D' km.
Since the lorry travelled at a speed of 60 km/h for 1.5 hours (from 11:00 a.m. to 12:30 p.m.) and then decreased its speed by 20 km/h, we can calculate the time it took for the lorry to reach town X.
Time taken at initial speed = Distance / Speed = D km / 60 km/h
Time taken at reduced speed = Distance / (60 km/h - 20 km/h) = D km / 40 km/h
Total time taken = Time taken at initial speed + Time taken at reduced speed
Since the total journey time for the car is the same as the total journey time for the lorry, we can equate the total time taken for both vehicles:
(Total journey time for the car) = (Total time taken for the lorry)
Let's calculate the journey time for the car first:
Journey time for the car = Distance / Speed = D km / 60 km/h
Equate the journey time for the car with the total time taken by the lorry:
D km / 60 km/h = (D km / 60 km/h) + (D km / 40 km/h)
Simplifying this equation, we get:
1 / 60 = 1 / 60 + 1 / 40
To solve this equation, we can find a common denominator:
1 / 60 = (2 / 120) + (3 / 120)
Now that we have a common denominator, we can add the fractions:
1 / 60 = 5 / 120
Since the left-hand side of the equation is in terms of hours (1 hour), we need to convert the right-hand side to hours as well:
5 / 120 = (5 / 120) * (1 hour / 60 minutes) = 5 / 240 = 1 / 48 hours
So, the time taken for the lorry to reach town X from the midpoint is 1/48 hours.
Since the lorry reached the midpoint at 12:30 p.m., we can add 1/48 hours to calculate the time it took for the lorry to reach town X:
Time lorry reached town X = 12:30 p.m. + 1/48 hours
Converting 1/48 hours to minutes, we get:
1/48 hours = (1/48) * 60 minutes = 1.25 minutes
Adding the minutes to the original time, we get the final answer:
Time lorry reached town X = 12:30 p.m. + 1.25 minutes
Therefore, the lorry reached town X at 12:31 p.m.