A car completes a journey in 10 minutes. For the first half of the distance the speed was 60km/h and for the second half the speed was 40km/h. How far is the journey?
TIme travelled = 10 minutes
Distance travelled = x
Speed 1 = 60kmph = 1km per minute
Speed 2 = 40kmph = 2/3 km per minute
x/2 covered @ 1 km per minute and x/2 covered at 2/3 km per minute
Time taken thus is
(x/2)/1 + (x/2)/(2/3) = 10
x/2 + (x/2)(3/2) = 10
x/2 + 3x/4 = 10
5x/4 = 10
x = (4/5)10 = 8
Thus distance is 8 km
Proof:
4km @ 1 km per minute takes 4 minutes
4km @ 2/3 km per minute takes 6 minutes
Thus total of 10 minutes
Distance travelled = x
Speed 1 = 60kmph = 1km per minute
Speed 2 = 40kmph = 2/3 km per minute
x/2 covered @ 1 km per minute and x/2 covered at 2/3 km per minute
Time taken thus is
(x/2)/1 + (x/2)/(2/3) = 10
x/2 + (x/2)(3/2) = 10
x/2 + 3x/4 = 10
5x/4 = 10
x = (4/5)10 = 8
Thus distance is 8 km
Proof:
4km @ 1 km per minute takes 4 minutes
4km @ 2/3 km per minute takes 6 minutes
Thus total of 10 minutes