SOLVE THE FOLLOWING NUMERICALS:-
A man travels 1200km apart by train and partly by car. It takes 28 hours and 94minutes if he travels 230 km by train and rest by car. It would take 80minutes more if he travels 160 km by train and the rest by the car/. Find the speed of the train and by car separately.
SOLVE THE FOLLOWING NUMERICALS:-
A man travels 1200km apart by train and partly by car. It takes 28 hours and 94minutes if he travels 230 km by train and rest by car. It would take 80minutes more if he travels 160 km by train and the rest by the car/. Find the speed of the train and by car separately.
Answers
Answer:
⇒x=100 and y=80
Hence, Speed of the train =100 km/hr
Speed of the car =80 km/hr.
Explanation:
Let the speed of the train be x km/hr and that of the car be y km/hr. We have following cases:
Case I When he travels 250 km by train and the rest by car.
In this case, we have
Time taken by the man to travel 250 km by train =
x
250
hrs
Time taken by the man to travel (370−250)=120km by car =
y
120
hrs
∴ Total time taken by the man to cover 370km =
x
250
+
y
120
It is given that the total time taken is 4 hours
∴
x
250
+
y
120
=4
⇒
x
125
+
y
60
=2 (i)
Case II When he travels 130 km by train and the rest by car:
In this case, we have
Time taken by the man to travel 130km by train =
x
130
hrs
Time taken by the man to travel (370−130)=240km by car =
y
240
hrs.
In this case, total time of the journey is 4 hrs 18 minutes.
∴
x
130
+
y
240
=4hrs 18 minutes
⇒
x
130
+
y
240
=4
60
18
⇒
x
130
+
y
240
=
10
43
.(ii)
Thus, we obtain the following system of equations:
x
125
+
y
60
=2
x
130
+
y
240
=
10
43
Putting
x
1
=u and
y
1
=v, the given system reduces to
125u+60v=2 (iii)
130u+240v=
10
43
(iv)
Multiplying equation (iii) by 4 the given system of equations becomes
500u+240v=8 ..(v)
130u+240v=
10
43
..(vi)
Subtracting equation (vi) from equation (v), we get
370u=8−
10
43
⇒370u=
10
37
⇒u=
100
1
Putting u=
100
1
in equation (v), we get
5+240v=8⇒240v=3⇒v=
80
1
Now, u=
100
1
and v=
80
1
⇒
x
1
=
100
1
and
y
1
=
80
1
⇒x=100 and y=80
Hence, Speed of the train =100 km/hr
Speed of the car =80 km/hr.
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