Question

A train starts from X and proceeds
towards y, which is at a distance of 55
km, at a speed of 40 kmph. After
covering a certain distance, it increases
its speed to 50 kmph and reaches Y in 1
hour 15 minutes after leaving X. After
how long does the train change its
speed?
A. 52 minutes
B.
45 minutes
C.
30 minutes
D.
38 minutes​

Answer 1

Answer:

As the train is moving at a constant speed until it changes to a different constant speed, its journey is governed by the equation,

s=v1t1+v2t2s=v1t1+v2t2

where ss is distance traveled, v1v1 and t1t1 are speed and time of the first half, and v2v2 and t2t2 are the same for the second half.

We know that the total time taken was 1 hour and 15 minutes, or 1.25 hours. We know that up until time t1t1 the train is moving at 40 km/h, and afterwards it is moving at 50km/h. Therefore we have s=55s=55, v1=40v1=40, v2=50v2=50, t2=1.25−t1t2=1.25−t1.

Hence putting these values into the above equation, we can solve for t1t1, the time at which the train changes speed.

40t1+50(1.25−t1)=5540t1+50(1.25−t1)=55

⟹62.5−10t1=

Just same as your question.

Answer 2

$\large\underline{\sf{Solution-}}$

↝ Let assume that the speed is changed after 't' hours.

Now,

According to statement,

↝ Total distance to be covered = 55 km

↝ Total time taken to cover 55 km = 1 hour 15 min = 75 min.

Now,

Case :- 1

• Speed of car = 40 km per hour

• Time taken = t hours

• Distance covered in t hours = 40t km

Case :- 2

• Speed of car = 50 km per hour

• Time taken = ( 5/4 - t ) hours

So,

• Distance covered in (5/4 - t) hours = 50(5/4 - t) km

According to statement,

Total distance covered = 55 km

$\rm :\longmapsto\:40t + 50\bigg(\dfrac{5}{4} - t\bigg) = 55$

$\rm :\longmapsto\:40t + 62.5 - 50t = 55$

$\rm :\longmapsto\:62.5 - 10t = 55$

$\rm :\longmapsto\: - 10t = 55 - 62.5$

$\rm :\longmapsto\: - 10t = - 7.5$

$\rm :\longmapsto\: 10t = 7.5$

$\rm :\longmapsto\: t = 0.75 \: hours$

$\rm :\longmapsto\: t = 0.75 \times 60 \: minutes$

$\bf\implies \:t = 45 \: minutes$

So, it implies the speed of the car changes after 45 minutes of the journey.

Formula Used :-

• 1. Distance = Speed × Time

• 2. 1 hour = 60 minutes.

Hence

$\: \: \: \: \: \: \: \: \: \: \: \: \: \underbrace{ \boxed{ \bf{ \: Option \: (B) \: is \: correct}}}$