Roohi travels 300 km to her home partly by train and partly by bus. She takes 4
hours if she travels 60 km by train and the remaining by bus. If she travels 100 km
by train and the remaining by bus, she takes 10 minutes longer. Find the speed of
the train and the bus separately.
Ye dekho ye tumhara points kha raha xD
Answers
solution:- let the speed of train and bus be u km/hr and v km/hr
according to the question :-
60/u + 240/v = 4 -------(I)
100/u + 200/u = 4 +10/ 60= 25/6 ----(II)
let 1/u = p and 1/v = q
the given equation reduce to
60p +240p =4 -----(III)
100p+ 200q = 25/6
600p + 2400p = 40 ------ (IV)
substating equation (IV) and (V)
1200q = 15
q = 15/1200 = 1/80
substating value of q in equation (III)
60p+ 3 = 4
60p = 1
p= 1/u = 1/60 , q = 1/v = 1/80
u = 60 km/h
v= 80 km/h
the speed of the train and the speed of bus are 60km/h and 80km/h
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SOLUTION
- Let the Speed of train be y and the speed of bus be x.
- Total times → 4 hours
→ 4 × 60
→ 240 mins
- Now,
→ 60/y + 240/x = 240
→ (60x + 240y)/xy = 240
→ 60x + 240y = 240xy
→ 60(x + 4y) = 240xy
→ x + 4y = 240xy/60
→ x + 4y = 4xy _(i)
→ 100/y + 200/x = 250
→ (100x + 200y)/xy = 250
→ 100x + 200y = 250xy
→ 50(2x + 4y) = 250xy
→ 2x + 4y = 250xy/50
→ 2x + 4y = 5xy _(ii)
- Subtract Eqn (ii) and (i) we get ;
→ y = 1
- Putting y = 1 in Eqn (i) , we get ;
→ x + 4y = 4xy
→ x + 4 × 1 = 4 × x × 1
→ x + 4 = 4x
→ 4 = 4x - x
→ 4 = 3x
→ x = 4/3
- Speed of bus = 4/3 × 60
→ 4 × 20
→ 80 km/hr.
- Speed of train (y) = 1 × 60
→ 60 km/hr.
- Hence, Speed of bus is 80 km/hr and speed of train is 60 km/hr.