MATHS * SOS *PLZ

Let the original speed be x m/s
the distance=1km=1000m
1min and 40s= 100s

the time needed if he runs at xm/s=1000/x
the time needed if he runs at 2x m/s=1000/2x

so

1000/x-1000/2x=100
2000-1000=200x
x=5

so his original speed=5 m/s

2008-05-24 11:29:19 補充：
if u want the ans in km/h:
because 1 km/h =1000m/3600s=5/18m/s
so 5 m/s =5/(5/18)km/h=18 km/h

Let X be the original speed.
1 min. 40 sec. ＝ 100 sec. ＝ 100 / 3600 hour


( I do not know how to type fraction, so the following is actually 3 fractions)


1 / X - 1 / 3X = 100 / 3600
( This is : 1 over X minus 1 over 3X = 100 over 3600 )

2008-05-24 11:23:24 補充：
1 / x - 1 / 3x = 100 / 3600
3 / 3x - 1 / 3x = 1 / 36
2 / 3x = 1 / 36
3x = 72
x = 24
He is travelling at a speed of 24 km/h

Let his original speed = v km/s
Since distance = 1 km, therefore time taken = 1/v sec.
New time = 1/v - 100.
Therefore, new speed = 1/(1/v - 100) which is 2 times faster, that is equals to 2v.
Therefore, the equation is :
1/(1/v - 100) = 2v
1 = 2v(1/v - 100)
1 = 2 - 200v
200v = 1
v = 1/200 km/s = 1000/200 m/s = 5m/s.