time speed distance

Question

A thief is spotted by a policeman from a distance of 100 meters when the policeman starts the chase the thief also starts running if the speed of the thief be 8 kmh and that of the policeman 10kmh how far the thief will have run before he is overtaken

Answer 1

distance=rate*time

d=rt

1 km=1000 m

100 m=1/10 km

(1/10)+x=(10)(t) for the policeman (x=distance the thief runs before being overtaken)

x=(8)(t) for the thief

substitute

(1/10)+8t=10t

1/10=10t-8t

1/10=2t

t=1/20 of an hour

(1/10)+x=(10)(1/20)

(1/10)+x=1/2

x=1/2-1/10

x=5/10-1/10

x=4/10 of a kilometer, or...

x=400 meters is how far the thief runs before being overtaken