(Q3).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, it takes 18 minutes more. Find the speed of the train and that of the car.

Let the speed of the train be x km. per hour and that of the car be y km. per hour.

Also, we know that time =
In situation 1, time spent travelling by train =
x
 hrs.
And time spent travelling by car =
y
 hrs.
So, total time taken = time spent in train + time spent in car =
x
 +
y

But, total time of journey is 4 hours, so

x
 +
y
 =
x
 +
y
 = ..................(1)

Again, when he travels 130 km by train and the rest by car

Time taken by him to travel 130 km by train =
x
 hrs.
Time taken by him to travel 240 km (370 - 130) by car =
y
 hrs.
Total time taken =
x
 +
y
But given, time of journey is 4 hrs 18 min i.e., 4
18
60
 hrs. = 4
hrs.
So,
x
 +
y
 =
...............(2)
Substitute
1
x
 = and
1
y
 = in equations (1) and (2)

a + b = ................(3)

a+ b =
.............(4)

For 60 and 240, LCM is . Using the elimination method,

Equation (3) × ⇒ a+b=
Equation (4) × ⇒ a+b =
(Same sign, so subtract)
(-) (-) (-)
a = -
=
-
=
a =
×
1
 =
1
Substitute a =
1
 in equation (3)
( 125 ×
1
 ) + 60b = 2
60b = 2 -
=
-
 =
b =
×
1
60
 =
1
So a =
1
 and b =
1
So
1
x
 =
1
 and
1
y
 =
1

x = km/hr and y = km/hr.

So, speed of the train was km/hr and speed of the car was km/hr.