Question

A man travels 600 km to his home ,partly by train and partly by bus.If he travels 120km by train and rest by bus it would take 8hours.If he travels 200km by train and rest by bus it will take 20 minutes more .find speed of train and bus saparetly.

Answer 1

Let the speed of the train be x km/h and speed of the bus be y km/h.

In case I:
If a man Travels 120 km by train, then
Distance covered by bus is (600-120)km = 480 km.
Time taken to cover 120 km by train = 120/x h.
Time taken to cover 480 km by bus = 480/y h.

[ Time = Distance/speed]

Total time of journey is 8 hours (GIVEN)
120/x + 480/y = 8
8(15/x +60/y) = 8
15/x +60/y = 1………..(1)

In case II:
If a man Travels 200 km by train, then
Distance covered by bus is (600-200)km = 400 km.
Time taken to cover 200 km by train = 200/x h.
Time taken to cover 400 km by bus = 400/y h.

[ Time = Distance/speed]

Total time of journey is 8 hours (GIVEN)
200/x + 400/y = 8 h 20 min

[ 8h 20 min = 8 (20/60) = 8 ⅓ h]
(200/x +400/y) = 25/3
25(8/x + 16/y) = 25/3
8/x + 16/y = ⅓
8(1/x +2/y) = ⅓
1/x +2/y = ⅓× ⅛

1/x +2/y = 1/24………..(2)

Putting 1/x = u and 1/y = v in eq i and ii,
15u + 60v = 1……… ….(3)
u + 2v =1/24…………..(4)

Multiply equation 4 by 15
15u + 30v = 15/24……….(6)

Subtract equation 6 from 3
15u + 60v = 1
15u + 30v = 15/24
(-) (-) (-)
------------------------
30v = -15/24 + 1

30v = (-15+24)/24
30v = 9/24
v = 9/(24× 30)
v = 3/(24×10)
v = 1/80

Putting v= 1/80 in equation 3
15u + 60v = 1
15 u + 60 (1/80)= 1
15u +3/4 = 1
15u = 1- 3/4
15 u = (4-3)/4
15 u = 1/4
u = 1 /(4×15)
u = 1/60

Now, u = 1/x = 1/60
x = 60
v = 1/y = 1/80
y = 80

Hence, a speed of train= 60km/h and speed of the bus= 80 km/h.

HOPE THIS WILL HELP YOU.