Question

a man travels 600km partly by train and partly by car. If he covers 400 km by train and rest by car, it takes him 20 hrs. But , if he travels 350 km by train and rest by car he takes 1 hr 15 mins longer. Find the speed of car and train?

Answer 1

let speed of bus be x km/hr.
let speed of car be y km/hr.
400/x+200/y=1200min.--------(1)
350/x+250/y=1275min.---------(2)
let 1/x=a 1/y=b
400a+200b=1200----------(1)
350a+250b=1275-----------(2)
taking 100 common from (1)
4a+2b=12-----------(1)
taking common 2
2a+b=6----------------------------------------(1)
taking 25 common from(2)
14a+10b=51-----------------------------------(2)
MULTIPLYING (1) BY 7
14a+7b=42
14a+10b=51
we get by elimination
-3b=-9
b=3 put in (1)
2a+3=6
2a=3
a=3/2
1/x=a
1/x=3/2. X=2/3
1/y=b
1/y=3. Y=1/3
SPEED OF BUS=2/3 km/hr.
SPEED OF CAR =1/3 km/hr.