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?

Answer 1

Try again

Answer 2

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.

Answer 3

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.