A train starts from X towards Y, which is at a distance of 55 km, at a speed of 40 km per hour. After some time it increases its speed to 50km/hr and reaches Y from X in 1 hour 15mins. after how much time did the train change its speed?
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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+v2t2
where s is distance traveled, v1 and t1 are speed and time of the first half, and v2 and t2 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 t1 the train is moving at 40 km/h, and afterwards it is moving at 50km/h. Therefore we have s=55, v1=40, v2=50, t2=1.25−t1.
Hence putting these values into the above equation, we can solve for t1, the time at which the train changes speed.
40t1+50(1.25−t1)=55
⟹62.5−10t1=55
⟹t1=0.75 hours
⟹t1=45 minutes
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