Question

Anand travels 400km partly by train and partly by bus. If he goes 300km by train and the
rest by bus, he reaches his destination in 7h 30 minutes. If he travels equal distance in each,
he reaches his destination 50 minutes later. Find the speed of the bus and the train.

Answer 1

Given : Anand travels 400km partly by train and partly by bus.

If he goes 300km by train and the rest by bus, he reaches his destination in 7h 30 minutes.

If he travels equal distance in each, he reaches his destination 50 minutes later.

To Find : the speed of the bus and the train.

Solution:

speed of the bus   = B km/hr

Speed of Train = T km/hr

Distance = Speed x Time

300km by train

Rest = 400 - 300 = 100 km by bus

Time taken = 300/T  + 100/B   =   7.5  hrs

equal distance in each

=> 200 km by train and 200 km by Bus

200/T  + 200/B  =   7.5 + 50/60  

=> 200/T  + 200/B  = 7.5 +  5/6

=>  400/T  = 7.5 - 5/6

=>  2400/T  = 40

=> T = 60

300/T  + 100/B   =   7.5

=> 5 + 100/B   =   7.5

=> B = 40

Train Speed = 60 km/hr

Bus Speed = 40 km/hr

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Answer 2

Given :-

• Anand travels 400km partly by train and partly by bus.
• If he goes 300km by train and the rest by bus, he reaches his destination in 7h 30 minutes.
• If he travels equal distance in each, he reaches his destination 50 minutes later.

To Find :-

• Speed of bus and the train ?

Solution :-

Let us assume that ,

• speed of bus = x km/h .
• speed of train = y km/h .

Case 1) :- 300 km by train and rest 100 km by bus .

→ Time = Distance / speed

so,

→ Time by train + Time by bus = 7(1/2)

→ (300/y) + (100/x) = (15/2)

→ 100{(3/y) + (1/x)} = 15/2

→ (3/y) + (1/x) = 3/40 ---------- Eqn.(1)

Case 2) :- 200 km by train and 200 km by bus .

→ 200/x + 200/y = 7:30 + 50

→ 200(1/x + 1/y) = (25/3)

→ (1/x) + (1/y) = (1/24) ---------- Eqn.(2)

now let,

• (1/x) = A
• (1/y) = B

then,

→ A + 3B = (3/40)

→ A + B = (1/24)

2B = (9 - 5)/120

→ 2B = 1/30

→ B = (1/60)

putting value of B we get,

→ A = (1/24) - (1/60) = (5 - 3)/120 = (2/120) = (1/60)

therefore,

• (1/x) = A => x = 60 km/h .
• (1/y) = B => y = 60 km/h .

Hence, Speed of Bus and train both is 60 km/h.

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