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 = [tex]\frac{\textrm{Distance}}{\textrm{TIme}}=\frac{1}{2.5}=0.4\ km/h[/tex]
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 [tex]\frac{5}{18}[/tex]. This gives,
[tex]0.4\times \frac{5}{18}=\frac{1}{9}\ m/s[/tex]
Now, distance of the hallway is equal to the product of speed and time. So,
Distance of hallway = Speed [tex]\times[/tex] Time
Distance of hallway = [tex]\frac{1}{9}\times 90=\frac{90}{9}=10\ m[/tex]
Therefore, the length of the hallway is 10 m.
