Mathematics

Question

A thief walks at a speed of 4 km/hr and can run at a speed of 5 m/s. He walked for some time until he saw a policeman and ran away. If he covered a total distance of 2.5 km in 20 min, find out how much distance had he walked and in how much time before he saw the policemen.

1 Answer

  • Answer:

      1 km in 15 min

    Step-by-step explanation:

    You want to know the walking time and distance if the walking speed is 4 km/h, and walking and running at 5 m/s combined to cover 2.5 km in 20 min.

    Time and distance

    Various units of time, distance, and speed are used here. We choose to convert all to km and hours.

    Let x represent the walking time in hours. The total time involved is 20 minutes = 1/3 hour. Then the running time in hours is (1/3 -x). The running speed in km/h is ...

      (5 m/s)·(3600 s/h)·(1 km/(1000 m)) = 18 km/h

    The total distance in km covered is ...

      distance = speed × time

      2.5 = (4 )(x) +(18)(1/3 -x)

      2.5 = 4x +6 -18x . . . . . . eliminate parentheses

      14x = 3.5 . . . . . . . . . . add 14x -2.5

      x = 3.5/14 = 1/4 . . . . hour (1/4 hour = 15 minutes)

    The walking distance was ...

      (4 km/h)(1/4 h) = 1 km

    The thief walked 1 km in 15 minutes before he saw the policeman.

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