Question

Two trains start moving at the same time from two stations towards each other at 50 km h-' and
65 km h-' respectively. When they meet, one train has travelled 52.5 km more than the other.
Find the distance between the two stations.
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Answer 1

Given :

Two trains start moving at the same time from two stations towards each other at 50 km h-' and 65 km h-' respectively. When they meet, one train has travelled 52.5 km more than the other.

To find :

• Distance between the two stations

Solution :

• Two trains start moving at the same time from two stations towards each other.

★ Speed of first train (A) = 50 km/h

★ Speed of second train (B) = 65 km/h

• When they meet, one train has travelled 52.5 km more than the other.

Let the distance of first train be x & second train be (52.5 + x)

As we know that

• In the case of train A

★ Speed = distance/time

→ Time = Distance/speed

→ T1 = x/50

• In the case of train B

→ Time = Distance/speed

→ T2 = 52.5 + x/65

Compare the both equations

→ x/50 = 52.5 + x/65

→ 50(52.5 + x) = 65x

→ 2625 + 50x = 65x

→ 2625 = 65x - 50x

→ 2625 = 15x

→ x = 2625/15

→ x = 175

•°• Distance travelled by train A = 175 km

•°• Distance travelled by train B = 52.5 + 175 = 227.5km

_______________________________

• The distance between the two stations

★ Distance travelled by train A + Distance travelled by B

→ 175 + 227.5

→ 402.5 km

•°• Distance between the two station = 402.5km

_______________________________

Answer 2

Answer:

Given :-

Two trains start moving at the same time from two stations towards each other at 50 km h-¹ and

65 km h-¹ respectively. When they meet, one train has travelled 52.5 km more than the other.

To Find :-

Distance between two station

Solution :-

Speed of train (A) = 50 km/hr

Speed of train (B) = 65 km/hr

Let the distance be y

$\huge \sf \: Time = \dfrac{Distance}{Speed}$

T(1) = y/50

T(2) = 52.5 + y/65

Now,

By comparing

y/50 = 52.5 + y/65

By cross multiplication

50(52.5 + y) = 65y

2625 + 50y = 65y

• (+ = -)

2625 = 65y - 50y

2625 = 15y

y = 2625/15

y = 525/3

y = 175

D1 = 175

D2 = 175 + 52.5 = 227.5 km

Now,

Distance = 227.5 + 175

Distance = 402.5 km