8. A man travels 600 km partly by train and partly by car. If he covers 400 km by train and
the rest by car, it takes him 6 hours and 30 minutes. But, if he travels 200 km by train and
the rest by car, he takes half an hour longer. Find the speed of the train and that of the car
ICBSE 2001)
Answers
x
1 Answer:
Let the speed of a train =xkm/hr
And the speed of a car =ykm/hr
Total distance travelled =600km
According to the question, If he covers 400km by train and rest by car i.e. (600−400)
=200km
Time take =6 hrs 30min =6+ 60 /30 =6.5 hrs
If he travels 200km by train and rest by car i.e. (600−200)
=400km
He takes half hour longer i.e. 7 hours
So, total time = train time + car time
We know that, time = distance / speed
⇒400 / x + 200 /y =6.5…(i)
⇒ 200 /x + 400 /y =7…(ii)
Let take
= u and
y
1
=v
400u+200v=6.5⋯(iii)
and 200u+400v=7…(iv)
On multiplying Eq.(iii) by 2 and Eq. (iv) by 4, we get 800u+400v=13…(a)
800u+1600v=28…(b)
On subtracting Eq.(a) from Eq. (b), we get 800u+1600v−800u−400v=28−13
⇒1200v=15
⇒v=
1200
15
⇒v=
80
1
On putting the value of v in Eq. (iv), we get
200u+400(
80
1
)=7
⇒200u+5=7
⇒200u=2
⇒u=
100
1
So, we get u=
100
1
and v=
80
1
⇒x=100 and y=80
Hence, the speed of the train is 100km/hr and the speed of the car is 80km/hr.
Step-by-step explanation: