A plane left 30minutes late than its schedued time and in order to reach of destination 1500km away in time .it had to increase its speed by 100 km/hr from the usual speed.find its usual speed.
Answers
Answer:
500 km/Hr
Step-by-step explanation:
Let say usual speed = S km/hr
time taken at usual speed = 1500/S
increased speed =S+100
time taken with increased speed = 1500/(S+100)
time saved = 30 minutes = 1/2 hr
1500/S - 1500/(S+100) = 1/2
1500(S+100-S) =(1/2) S (S+100)
300000 = S^2 + 10S
S^2 + 100S = 300000
S^2 + 600S -500S - 300000 = 0
(S+600)(S-500) = 0
S = 500 km /Hr as it can not be negative
Solution :-
Let the original speed of train be x km/hr
New speed = (x + 100) km/hr
We know that,
Time = Distance / Speed
Given : A plane left 30 minutes or 1/2 hours later than the scheduled time.
According to the question,
=> 1500/x - 1500/(x + 100) = 1/2
=> (1500x + 15000 - 1500x)/x(x + 100) = 1/2
=> 2(15000) = x(x + 100)
=> 30000 = x² + 100x
=> x² + 100x - 30000 = 0
=> x² + 600x - 500x - 30000 = 0
=> x(x + 600) - 500(x + 600) = 0
=> (x - 500) (x + 600) = 0
=> x = 500 or x = - 600
∴ x ≠ - 600 (Because speed can't be negative)
Hence,
Its usual speed = 500 km/hr