Answer:
1 hour
Step-by-step explanation:
The distance covered by each of the two vehicle can be written as
![d=vt](https://tex.z-dn.net/?f=d%3Dvt)
where
d is the distance covered
v is the speed of the vehicle
t is the time elapsed
For the bus, the speed is
![v_b = 60 mph](https://tex.z-dn.net/?f=v_b%20%3D%2060%20mph)
So the distance covered by the bus in a time t is
(1)
The kids in the bus took 3 hours to reach the camp,
t = 3 h
So the distance between the school and the camp is:
![d=(60)(3)=180 mi](https://tex.z-dn.net/?f=d%3D%2860%29%283%29%3D180%20mi)
For the truck, the speed is
![v_t=45 mph](https://tex.z-dn.net/?f=v_t%3D45%20mph)
So the distance covered by the truck in a time t is
(2)
Since the distance to cover is 180 miles, the time taken by the truck is
![t=\frac{d}{45}=\frac{180}{45}=4 h](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bd%7D%7B45%7D%3D%5Cfrac%7B180%7D%7B45%7D%3D4%20h)
And so, the truck arrives
![\Delta t = t_t - t_b = 4 h - 3 h = 1 h](https://tex.z-dn.net/?f=%5CDelta%20t%20%3D%20t_t%20-%20t_b%20%3D%204%20h%20-%203%20h%20%3D%201%20h)
1 hour after the bus.