Given :
Distance between P and Q = 100 km
Speed of bus = 20 % more than that of car
To find:
Speed of car
Solution:
Let us take the speed of the car as X and the speed of the bus as Y.
Speed of bus ( Y ) = 20 % more than speed of car
Y = X + (20/100) X
Y = (120/100) X
Y = ( 6/5 ) X
As, Speed = Distance / time
From here,
Time taken by car ( t₁ ) = ( 100 / X) Hours
Time taken by bus ( t₂ ) = [tex]\frac{500}{6 X}[/tex] Hours = [tex]\frac{250}{3X}[/tex] Hours
Since, both the vehicles reach point Q at the same time with bus losing additional 5 minutes (i.e. 1/12 hours) while stopping at the station,
the equation for both the bus and car can be written as,
[tex]\frac{100}{X}[/tex] = [tex]\frac{250}{3 X}[/tex] + [tex]\frac{1}{12}[/tex]
X = 200 km per hour
Hence the speed of the card is 200 km/h