reeta travels a distance of 370km partly by bus and partly by car when she travels 250 km by bus and rest by car takes 8 hours to reach her destination if she travels 200km by bus and rest by car take 15 minutes longer find the speed of the bus and car
Answers
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.