Question

A man travels 600 km to his home partly by train and partly by bus. He takes 8 hours, if he travels 120 km by train and rest by bus. Further, it takes 20 minutes longer, if he travels 200 km by train and rest by bus. Find the speeds of the train and the bus.

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...

Answer 2

Answer:

80 and 60 km

Step-by-step explanation:

Solving the blow eq.will give your answer

I/x=1/80

And

1/y=1/60 km

So hence answer is

80km

And

60km