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.