Man Travels 370 km partly by train and partly by car if we cover 250 km by train and other days it takes 4 hours but if he travelled 130 km by train and the rest by the car it takes 18 minutes longer find the speed of the train and that of the car
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Answer:
The speed of the train is 100 km/hr and speed of the car is 80 km/hr. Solution: Let the speed of the train be 'x' km/hr and the speed of the car be 'y' km/hr. Also it is given that he travels 200 km by train and the rest i.e. (600-200) = 400 km by car and the time taken is half an hour longer
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A man travels 370 km partly by train and partly by car. If he covers 250 km by train and the rest by car, it takes him 4 hours. But, if he travels 130 km by train and the rest by car, he takes 18 minutes longer. Find the speed of the train and that of the car.
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Answer
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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