SOLUTION: Roohi travels 300km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and remainin

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Roohi travels 300km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and remainin      Log On


   

Question 889908: Roohi travels 300km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and remaining by bus. If she travels 100 km by train and remaining by bus she takes 10 minutes longer. Find the speed of train and bus.
Answer by charu91(7) About Me  (Show Source):
You can put this solution on YOUR website!
Total distance travelled be Roohi=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