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.
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?
3 answers
Try again
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.