Question

Kimi travels 300 km to her home partly by bus and partly by train. She takes 4 hours if she travelled 60 km by train and remaining by bus. If she travelled 100 km by train and remaining by bus, She would take 10 minutes longer. Find average speed of bus and train.

Answer 1

Total distance travelled be kimi=300
Let speed of train be x
Let speed of bus bus be y
Travelling 60km by train and rest by bus she took 4 hours to cover 300km
Travelling 100km by train and rest by train she took 4 hours and 10 minutes.
Putting this relations into eqn, we get,
60/x+240/y=300
100/x+200/y=300
Rearranging the above eqns
60y+240x=300xy→(1)
100y+200x=300xy→(2)
Divide first eqn by 60
y+4x=5xy→(3)
Divide second by 50
2y+4x=6xy→(4)

Subtracting (3) from (4)
2y+4x=6xy
-y-4x=-5xy
Gives x=1km/min
=60km/hr
From eqn

60/x+240/y=4
60/60+240/y=4
240/y=4-1
240/3=y
y=80km/hr
Speed of train is 60km/hr
Speed of bus is 80km/hr