16. A train has to travel the distance between Aurang abad and Daulatabad, equal to 20 km, at a constans speed. It travelled half the way with the specified speed and stopped for three minutes, to arrive at Daulatabad on time, it had to increase its speed by 10 km/h for the rest of the way. Next time the train stopped half-way for five minutes. By what speed must it increase its speed for the remaining half of thedistance to arrive at Daulatabad as per the schedule?
Answers
Given : A train has to travel the distance between Aurang abad and Daulatabad, equal to 20 km, at a constans speed. It travelled half the way with the specified speed and stopped for three minutes, to arrive at Daulatabad on time, it had to increase its speed by 10 km/h for the rest of the way. Next time the train stopped half-way for five minutes.
To Find : By what speed must it increase its speed for the remaining half of the distance to arrive at Daulatabad as per the schedule?
Solution:
Distance = 20 km
Half Distance =10 km
Speed = S km /hr
Time Taken = 20 / S hrs
Time taken for half way = 10/S hr
Stop = 3 mins = 1/20 hrs
Time taken for rest half way = 10 / (S + 10) hrs
10/S + 1/20 + 10/(S + 10) = 20/S
=> 1/20 = 10/S - 10/(S + 10)
=> S (S + 10) = 20 * 10 ( S + 10 - S)
=> S² + 10S = 2000
=> S² + 10S - 2000 = 0
=> (S + 50)(S - 40) = 0
=> S = 40 Speed = 40 km
Time Taken = 20 / S hrs = 20/40 = 1/2 hrs = 30 min
Half way = 15 min
Rest Distance = 10 km . Rest time = 15 - 5 = 10 mins = 1/6 hrs
Speed = 10/ (1/6) = 60 km/hr
Hence Speed to be increased by 20 km/hr
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