Question
A truck left the station at 6 am going at 45 km/hr. A van left the same place 2 hours later heading in the same direction at 54 km/hr. At what time will the van catch up with the truck?
Answers
GPT 3.5
To solve this problem, we need to find the time it takes for the van to catch up with the truck.
Since the van left 2 hours later than the truck, this means that the van had a head start of 45 km/h * 2 h = 90 km.
Let t be the time it takes for the van to catch up with the truck.
During this time, the truck will have traveled a distance of 45 km/h * t, and the van will have traveled a distance of 54 km/h * t.
Since the van catches up with the truck, the distance traveled by the truck and the van must be equal:
45 km/h * t = 54 km/h * t + 90 km.
Subtracting 54 km/h * t from both sides of the equation, we get:
45 km/h * t - 54 km/h * t = 90 km.
Simplifying the left side of the equation, we find:
-9 km/h * t = 90 km.
Dividing both sides of the equation by -9 km/h, we get:
t = -90 km / -9 km/h = 10 h.
Therefore, the van will catch up with the truck 10 hours after the van left, which means at 6 am + 10 h = 4 pm.
Therefore, the van will catch up with the truck at 4 pm.
Since the van left 2 hours later than the truck, this means that the van had a head start of 45 km/h * 2 h = 90 km.
Let t be the time it takes for the van to catch up with the truck.
During this time, the truck will have traveled a distance of 45 km/h * t, and the van will have traveled a distance of 54 km/h * t.
Since the van catches up with the truck, the distance traveled by the truck and the van must be equal:
45 km/h * t = 54 km/h * t + 90 km.
Subtracting 54 km/h * t from both sides of the equation, we get:
45 km/h * t - 54 km/h * t = 90 km.
Simplifying the left side of the equation, we find:
-9 km/h * t = 90 km.
Dividing both sides of the equation by -9 km/h, we get:
t = -90 km / -9 km/h = 10 h.
Therefore, the van will catch up with the truck 10 hours after the van left, which means at 6 am + 10 h = 4 pm.
Therefore, the van will catch up with the truck at 4 pm.
Try again
GPT 3.5
Let's consider the time it takes for the van to catch up to the truck as t.
In that time, the truck would have traveled a distance of 45 km/h * t, and the van would have traveled a distance of 54 km/h * (t - 2) since the van left 2 hours later.
To find the time when the van catches up with the truck, we need to equate the distances traveled by both vehicles:
45 km/h * t = 54 km/h * (t - 2).
Now let's solve for t:
45t = 54(t - 2).
Expanding the equation:
45t = 54t - 108.
Subtracting 54t from both sides:
-9t = -108.
Dividing both sides by -9:
t = 12.
Therefore, the van will catch up with the truck 12 hours after the truck left, which is at 6 am + 12 h = 6 pm.
Hence, the van will catch up with the truck at 6 pm.
In that time, the truck would have traveled a distance of 45 km/h * t, and the van would have traveled a distance of 54 km/h * (t - 2) since the van left 2 hours later.
To find the time when the van catches up with the truck, we need to equate the distances traveled by both vehicles:
45 km/h * t = 54 km/h * (t - 2).
Now let's solve for t:
45t = 54(t - 2).
Expanding the equation:
45t = 54t - 108.
Subtracting 54t from both sides:
-9t = -108.
Dividing both sides by -9:
t = 12.
Therefore, the van will catch up with the truck 12 hours after the truck left, which is at 6 am + 12 h = 6 pm.
Hence, the van will catch up with the truck at 6 pm.