Case study:
An Air India flight from Mumbai to Colombo was delayed by 60 minutes due to emergency landing of the plane in Vizag as a passengers in the flight suddenly had a cardiac arrest. Now to reach destination of 1800 km from Vizag to Colombo in time, so that passengers could catch their connecting flights, the speed of the plane was increased by 300 km/h than the usual speed.
Based on the above information, answer the following questions :
(i) Taking the usual speed of plane as x km/h, form quadratic equation for situation described above.
(ii) Find the nature of the roots of the quadratic equation.
(iii) Find the usual speed of the plane.

Question

Case study:
An Air India flight from Mumbai to Colombo was delayed by 60 minutes due to emergency landing of the plane in Vizag as a passengers in the flight suddenly had a cardiac arrest. Now to reach destination of 1800 km from Vizag to Colombo in time, so that passengers could catch their connecting flights, the speed of the plane was increased by 300 km/h than the usual speed.

An Air India flight from Mumbai to Colombo was delayed by 60 minutes due to emergency landing of the plane in Vizag as a passengers in the flight suddenly had a cardiac arrest. Now to reach destination of 1800 km from Vizag to Colombo in time, so that passengers could catch their connecting flights, the speed of the plane was increased by 300 km/h than the usual speed. Quadratic equations, Concise Mathematics Solutions ICSE Class 10.

Based on the above information, answer the following questions :

(i) Taking the usual speed of plane as x km/h, form quadratic equation for situation described above.

(ii) Find the nature of the roots of the quadratic equation.

(iii) Find the usual speed of the plane.

KnowledgeBoat · Accepted Answer

(i) Let the usual speed of the plane be x km/hr. Distance from Vizag to Colombo = 1800 km Time taken at usual speed = hr Increased speed = x + 300 Time taken at increased speed = hr Since flight delayed by 60 minutes = 1 hour, Solving, Hence, the required equation is x2 + 300x - 540000 = 0. (ii) Comparing x2 + 300x - 540000 = 0 with ax2 + bx + c = 0 we get, a = 1, b = 300 and c = -540000. We know that, D = b2 - 4ac = (300)2 - 4(1)(-540000) = 90000 + 2160000 = 2250000 D 0 Hence, roots are real and unequal. (iii) Comparing x2 + 300x - 540000 = 0 with ax2 + bx + c = 0 we get, a = 1, b = 300 and c = -540000. We know that, x = Substituting values of a, b and c in above equation we get, Speed cannot be negative, x = 600 km/h Hence, usual speed of the plane = 600 km/h.

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