Question

a plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time,it had to increase it's speed by 100km/h from the usual speed . find its usual speed

Answer 1

distance to be travelled by plain = 1500km
speed of plane be x km/hr
time taken = 1500/x km/hr
now;
distance to be travelled by plain = 1500km
speed of plane = x+100km/hr
time taken = 1500/x+100 hr

1500/x - 1500/x+100 = 1/2
1500(x+100) - 1500x = 1/2(x)(x+100)
2[1500x+1500(100)-1500x]=x^{2}+100x
3000(100) =x^{2}+100x
 x^{2} +100x-3000(100)=0
 x^{2} +600x-500x-300000=0
(x+600)(x-500)=0
x=-600;x=500
since speed cannot be negative 
hence usual speed of plane = 500km/hr

Answer 2

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