A train travelling at a uniform speed of 360 km
would have taken 48 min less to travel the same
distance, if its speed were 5km/h more. Find the
original speed of the train.
Answers
Answer:
Step-by-step explanation:
Let initial speed of train be x km/hr.
Distance travelled = 360 km.
//we know that Speed = Distance/time => Time = Distance /Speed.
Time taken by train Initially = 360/x.
If speed is increased by 5 km/hr,
Time taken by train = 360/x+5.
Difference in time taken = 48/60 hr.
=> 360/x - 360/x+5 = 48/60
=> 360(1/x - 1/x+5) = 48/60
=> 360[x + 5 - x / x(x+5)] = 48/60
=> 360 * 5/x(x+5) = 48/60
=> x(x+5) = 360 * 5 * 60 / 48
=> x² + 5x = 2250
=> x² + 5x - 2250 = 0
=> x² + 50x - 45x - 2250 = 0
=>x(x+50) - 45(x+50) = 0
=> (x - 45)(x + 50) = 0
=> x = 45 or -50.
Since x cannot be negative, x= 45 km/hr.
Thus original speed of train = 45 km/hr.
Step-by-step explanation:
Let initial speed of train be x km/hr.
Distance travelled = 360 km.
//we know that Speed = Distance/time => Time = Distance /Speed.
Time taken by train Initially = 360/x.
If speed is increased by 5 km/hr,
Time taken by train = 360/x+5.
Difference in time taken = 48/60 hr.
=> 360/x - 360/x+5 = 48/60
=> 360(1/x - 1/x+5) = 48/60
=> 360[x + 5 - x / x(x+5)] = 48/60
=> 360 * 5/x(x+5) = 48/60
=> x(x+5) = 360 * 5 * 60 / 48
=> x² + 5x = 2250
=> x² + 5x - 2250 = 0
=> x² + 50x - 45x - 2250 = 0
=>x(x+50) - 45(x+50) = 0
=> (x - 45)(x + 50) = 0
=> x = 45 or -50.
Since x cannot be negative, x= 45 km/hr.
Thus original speed of train = 45 km/hr.