ved travels 600 kilometre to his home partly by train and partly by car he takes 8 hours if he travels 120 km by train and the rest by car he takes 20 minutes longer if he travel 200 km by train and rest by car find the speed of train and car
Answers
Step-by-step explanation:
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.
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