She takes 4 hours if she travels 60 km by train by remaining by bus
If she travels 100 km by train and remaining by bus, she takes 10 minutes longer.
Find the speed of train and bus separately.
Soln.
Let the speed of the train be x km/hr and the speed of the bus be y km/hr
Total Distance = 300 km
Let us understand this sum in tabular form
| Train | Bus |
| | |
| | |
| | |
Distance
Speed
Time
60 km
240 km
Total Distance = 300km
By train = 60 km
Hence,
by bus = 300 – 60 = 240 km
x km / hr
y km / hr
Time = Distance
Speed
60
x
hr
240
y
hr
Total Time = 4 hours
According to the first condition
60
x
+
240
y
=
4
| Train | Bus |
| | |
| | |
| | |
Distance
Speed
Time
100 km
200 km
x km / hr
y km / hr
100
x
hr
200
y
hr
According to the second condition
She takes 10 minutes longer
10 minutes = 10 hrs
60
New time = 4 + 10
60
New time = 4 + 1 = 25 hrs
6 6
100
x
+
200
y
=
25
6
Dividing throughout by 4
15
x
+
60
y
=
1
... (i)
Dividing throughout by 25
4
x
+
8
y
=
... (ii)
1
6