Question:
A plane left 30minutes later from its scheduled time.In order to reach its destination 1500 km away on time ,it has to increase it's speed 250km/hr from its usual speed .find its usual speed.
Answer:
Let the usual speed of the plane is x km/hr
Increased speed of the plane = (x + 250) km/hr
Now, time taken to reach the destination at usual speed = 1500/x hr
and time taken to reach the destination at increased speed = 1500/(x + 250) hr
Given, diffrence of time = 30 minutes
=> 1500/x - 1500/(x + 250) = 30/60 {since 30 minutes = 30/60 hours}
=> 1500/x - 1500/(x + 250) = 1/2
=> {1500*(x + 250) - 1500x}/{x*(x + 250)} = 1/2
=> {1500x + 1500*250 - 1500x}/(x2 + 250x) = 1/2
=> 1500*250/(x2 + 250x) = 1/2
=> 1500*250*2 = x2 + 250x
=> x2 + 250x = 750000
=> x2 + 250x - 750000 = 0
=> x2 + 1000x - 750x - 750000 = 0
=> x(x + 1000) - 750(x + 1000) = 0
=> (x + 1000)*(x - 750) = 0
=> x = -1000, 750
Since speed can not be negative
So, x = 750
Hence, the usual speed of the plane is 750 km/hr
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