Question

A robot moving forward at a constant speed takes 2.5 hours to travel 1 kilometer. Moving forward at this same constant speed, it takes the robot 90 seconds to travel the length of a particular hallway. How many meters long is the hallway?

Answer 1

The length of the hallway is 10 m.

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}}=(1)/(2.5)=0.4\ km/h`

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
`(5)/(18)`. This gives,

`0.4* (5)/(18)=(1)/(9)\ m/s`

Now, distance of the hallway is equal to the product of speed and time. So,

Distance of hallway = Speed
`*` Time

Distance of hallway =
`(1)/(9)* 90=(90)/(9)=10\ m`

Therefore, the length of the hallway is 10 m.