Answer:
The length of the hallway is 10 m.
Step-by-step explanation:
Given:
Time taken to cover 1 km = 2.5 hours
Distance covered in 2.5 hours = 1 km
Therefore, speed of robot = ![\frac{\textrm{Distance}}{\textrm{TIme}}=\frac{1}{2.5}=0.4\ km/h](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextrm%7BDistance%7D%7D%7B%5Ctextrm%7BTIme%7D%7D%3D%5Cfrac%7B1%7D%7B2.5%7D%3D0.4%5C%20km%2Fh)
Now, speed is constant.
Now, time taken to cover the length of hallway = 90 s
Speed of the robot = 0.4 km/h
Converting 0.4 km/h to m/s, we multiply by the factor
. This gives,
![0.4\times \frac{5}{18}=\frac{1}{9}\ m/s](https://tex.z-dn.net/?f=0.4%5Ctimes%20%5Cfrac%7B5%7D%7B18%7D%3D%5Cfrac%7B1%7D%7B9%7D%5C%20m%2Fs)
Now, distance of the hallway is equal to the product of speed and time. So,
Distance of hallway = Speed
Time
Distance of hallway = ![\frac{1}{9}\times 90=\frac{90}{9}=10\ m](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B9%7D%5Ctimes%2090%3D%5Cfrac%7B90%7D%7B9%7D%3D10%5C%20m)
Therefore, the length of the hallway is 10 m.