A messenger traveling 65 miles per hour pursues a truck which has a start of 2 hours and overtakes it in 3 hours. Find the trucks’ speed?

65*3 = 5x

x = 39

To find the truck's speed, we can use the concept of relative speed.

Let's assume the truck's speed as 'T' miles per hour.

The messenger traveled for a total of 3 hours and covered a distance of 65 miles.
So, the distance covered by the messenger is 65 miles.

The truck had a head start of 2 hours. Therefore, it traveled for a total of 3 + 2 = 5 hours.
Let's calculate the distance covered by the truck in those 5 hours.

Distance = Speed * Time
Distance covered by the truck = T * 5 miles

Since the messenger catches up with the truck, the distance covered by both should be the same.

65 miles = T * 5 miles

Now, let's solve this equation to find the truck's speed (T):

65 = 5T

Dividing both sides of the equation by 5:
13 = T

Therefore, the truck's speed is 13 miles per hour.

To find the truck's speed, we can use the formula:

Distance = Speed × Time

Let's say the truck's speed is "x" miles per hour.

The messenger traveled for 3 hours at a speed of 65 miles per hour, so the distance covered by the messenger is:

Distance_messenger = Speed_messenger × Time_messenger
Distance_messenger = 65 × 3

The truck had a head start of 2 hours, so it traveled for a total of 3 - 2 = 1 hour.

The distance covered by the truck is:
Distance_truck = Speed_truck × Time_truck
Distance_truck = x × 1

Since the messenger catches up to the truck, the distance traveled by both the messenger and the truck is the same:

Distance_messenger = Distance_truck
65 × 3 = x × 1

Simplifying the equation:

195 = x

Therefore, the truck's speed is 195 miles per hour.