A truck travels at a speed of 64 km / h heading towards Town A. 3 hours later a jeep travelling at a speed of 96 km / h begins its journey from the same place . When does the jeep catch up with the truck ?
To find out when the jeep catches up with the truck, we need to determine the time it takes for the jeep to cover the same distance as the truck.
Let's denote the time it takes for the jeep to catch up with the truck as "t."
During the 3-hour head start that the truck has, it would have already covered a distance of (64 km/h) * (3 hours) = 192 km.
So, when the jeep starts its journey, it needs to cover a distance of 192 km to catch up with the truck.
Since the truck is traveling at a speed of 64 km/h and the jeep is traveling at a speed of 96 km/h, the relative speed between the jeep and the truck is (96 km/h - 64 km/h) = 32 km/h.
Using the formula distance = speed * time, we can write:
192 km = 32 km/h * t
Now, we can solve for t:
t = 192 km / 32 km/h
= 6 hours
Therefore, the jeep will catch up with the truck after 6 hours.
To find out when the jeep catches up with the truck, we can use the concept of relative speed.
Let's assume that the time it takes for the jeep to catch up with the truck is 't' hours.
In the 3 hours that the truck has already been traveling, it has covered a distance of 64 km/h x 3 h = 192 km.
Now, when the jeep starts, the distance between the jeep and the truck is 192 km (since the jeep hasn't covered any distance yet).
Since both the truck and the jeep are traveling in the same direction, the relative speed between them is the difference of their speeds, which is 96 km/h - 64 km/h = 32 km/h.
To catch up the initial distance of 192 km at a relative speed of 32 km/h, it would take the jeep t hours.
Therefore, we can set up the equation:
32 km/h x t = 192 km
Dividing both sides of the equation by 32 km/h:
t = 192 km / 32 km/h
t = 6 hours
Hence, the jeep catches up with the truck after 6 hours of the jeep's journey.
Assuming the jeep travels the same route as the truck, then
they meet after x hours, where
64x = 96(x-3)