iii) 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.
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Answers
Solution:-
Let the speed of train and bus be u km/h and v km/h.
According to the question:
60/u + 240/v = 4 ... (i)
100/u + 200/v = 25/6 ... (ii)
Putting 1/u = p and 1/v = q in the equations, we get
⇒ 60p + 240q = 4 ... (iii)
⇒ 100p + 200q = 25/6
⇒ 600p + 1200q = 25 ... (iv)
Multiplying equation (iii) by 10, we get
⇒ 600p + 2400q = 40 .... (v)
Subtracting equation (iv) from (v), we get 1200q = 15
⇒ q = 15/200 = 1/80 ... (vi)
Putting equation (iii), we get
⇒ 60p + 3 = 4
⇒ 60p = 1
⇒ p = 1/60
⇒ p = 1/u = 1/60 and q = 1/v = 1/80
⇒ u = 60 and v = 80
Speed of train = 60 km/h
Speed of bus = 80 km/h.
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Step-by-step explanation:
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.