THE DISTANCE BETWEEN A AND B IS 150KM.A CAR STARTS FROM A AT 10PM AND TRAVELS AT AN AVERAGE SPEED OF 80KM/H TOWARDS TOWN B.A TRANSIT LORRY TRAVELS FROM TOWN B AT 10:15AM TOWARDS TOWN A AT AN AVERAGE SPEED OF 40KM/H.AT WHAT TIME WILL THE TWO VEHICLES MEET?
Before 10:15, only car is on the road, by which time it has travelled 80*(15/60)=20 km towards B.
So remaining distance as of 10:15 is 150-20=130 km.
When lorry starts, they approach each other at a total speed of (80+40)=120 km/h.
Elapsed time (since 10:15) when they meet is therefore
= 130/(80+40)=1h05m
You can work out the meeting time from here.
To find out at what time the two vehicles will meet, we need to calculate the time it takes for each vehicle to travel the given distance.
Let's start with the car:
The car starts at 10 PM and travels towards town B at an average speed of 80 km/h. The distance between A and B is 150 km. So, we can calculate the time it takes for the car to travel from A to B using the formula:
Time = Distance / Speed
Time = 150 km / 80 km/h = 1.875 hours
Next, let's calculate the time for the transit lorry:
The lorry starts from town B at 10:15 AM and travels towards town A at an average speed of 40 km/h. We can calculate the time it takes for the lorry to travel from B to A using the same formula:
Time = Distance / Speed
Time = 150 km / 40 km/h = 3.75 hours
Now, we need to find the total time from when the car starts at 10 PM to when the lorry arrives at the meeting point.
The car takes 1.875 hours (1 hour and 52.5 minutes) to reach the meeting point.
We know that the lorry starts 15 minutes (0.25 hours) after the car. So, we need to add this time to the car's travel time to find out when both vehicles will meet:
Total Time = Car's Travel Time + Lorry's Start Time
Total Time = 1.875 hours + 0.25 hours = 2.125 hours
Therefore, the two vehicles will meet approximately 2 hours and 8.5 minutes after the car starts.
As the car starts at 10 PM, we can add 2 hours and 8.5 minutes to find out the meeting time:
10 PM + 2 hours + 8.5 minutes = 12:08:30 AM
So, the two vehicles will meet at approximately 12:08:30 AM.