A plane left 20 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100km/h from the usual speed. Find its usual speed.
parmarfreya12:
its from board paper
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Let the usual speed of the plane = x km/hr
Increased speed of the plane = (x + 100) km/hr
Time take to reach the destination at the usual speed, t1 = 1500xhr
Time take to reach the destination at the increased speed, t2 = 1500x+100hr
Difference of both the times = t1 - t2 = 30 mins = 1/2 hr
1500x-1500x+100 = 12⇒1500(x+100) - 1500x =x(x+100)2⇒1500x + 150000 -1500x =x(x+100)2⇒300000= x2+100x⇒x2+100x -300000=0⇒x2+600x-500x -300000=0⇒(x+600)(x-500)=0x=500 or x=-600
As speed cannot be negative so x = 500 km/hr.
Hence, the usual speed of the plane is 500 km/hr
Increased speed of the plane = (x + 100) km/hr
Time take to reach the destination at the usual speed, t1 = 1500xhr
Time take to reach the destination at the increased speed, t2 = 1500x+100hr
Difference of both the times = t1 - t2 = 30 mins = 1/2 hr
1500x-1500x+100 = 12⇒1500(x+100) - 1500x =x(x+100)2⇒1500x + 150000 -1500x =x(x+100)2⇒300000= x2+100x⇒x2+100x -300000=0⇒x2+600x-500x -300000=0⇒(x+600)(x-500)=0x=500 or x=-600
As speed cannot be negative so x = 500 km/hr.
Hence, the usual speed of the plane is 500 km/hr
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