rahim travels 600 km to his home partly by train and partly by car he takes 8 hours if he travels 120 km by train and rest by car.He takes 20 minutes more if he travels 200 km by train and rest by car.Find the speed of the train and the car
Answers
Answer:
Case 1 : Total distance =600 km
distance covered by train =120 km
time taken by train =120/x km/h
x= speed of the train
Distance covered by car =(600−120)=480 km
Time taken by car =(
y
480
) km/h
total time taken =
x
120
+
y
480
=8
x
30
+
y
120
=2
Case II :
total distance covered by train =200 km
total time taken by train =200/x
total distance covered by car =600−200=400
total time taken by car =
y
400
km/h
total time taken =8×(20/60)=25/3
x
200
+
y
400
=
3
25
⇒600/x+
y
1200
=25
Let 1/x be u and
y
1
be v
equation are then
600u+1200v=25⇒30u+120v=2
multiplying equation (1) by 20 and substrating the equations we get :
1200v=15,v=15/1200
Since, 1/y ⇒y=
15
1200
=80 km/h
speed of car =
80 km/h
multiplying equation (1) on 10 and substracting equations we get
300u=5
u=5/300⇒1/x=u
speed of train =x=
5
300
=60 km/h