A van left Town X for Town Y at 07 00 and passed by a school 99 km away at 10 18. A car left Town X in the same direction at 10 00 and passed the same school at 11 30. How long did it take for the car to pass by the van?
Question
A van left Town X for Town Y at 07 00 and passed by a school 99 km away at 10 18. A car left Town X in the same direction at 10 00 and passed the same school at 11 30. How long did it take for the car to pass by the van?
Solution
First, let's calculate the speed of the van and the car.
The van traveled 99 km in 3 hours and 18 minutes. To make the calculation easier, let's convert 3 hours and 18 minutes to minutes only. 3 hours is 180 minutes and if we add the 18 minutes, we get a total of 198 minutes. So, the speed of the van is 99 km / 198 minutes = 0.5 km/minute.
The car traveled the same distance, 99 km, but in 1 hour and 30 minutes. Again, let's convert this to minutes. 1 hour is 60 minutes and if we add the 30 minutes, we get a total of 90 minutes. So, the speed of the car is 99 km / 90 minutes = 1.1 km/minute.
Now, let's calculate when the car will pass the van. The car started 2 hours (or 120 minutes) after the van. In this time, the van would have traveled 120 minutes * 0.5 km/minute = 60 km.
So, when the car starts, it has 60 km to catch up to the van. The car is traveling at 1.1 km/minute and the van is traveling at 0.5 km/minute, so the car is catching up at a rate of 1.1 km/minute - 0.5 km/minute = 0.6 km/minute.
To find out how long it takes for the car to pass the van, we divide the distance it needs to catch up by the rate it's catching up: 60 km / 0.6 km/minute = 100 minutes.
So, it took 100 minutes (or 1 hour and 40 minutes) for the car to pass by the van.
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