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Question

An aeroplane takes 1 hour less for a journey of 1200km if its speed is increased by 100 km/hr from its usual speed of the plane.

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Solution

Let the usual speed of plane be x km/hr,

Then the increased speed of the plane is = (x + 100) km/hr

Time taken by the plane under usual speed to cover 1200km = 1200 over x hr

Time taken by the plane under increased speed to cover 1200 km = fraction numerator 1200 over denominator x plus 100 end fractionhr

Therefore,

1200 over x � fraction numerator 1200 over denominator left parenthesis x plus 100 right parenthesis end fraction equals 1
fraction numerator 1200 left parenthesis x plus 100 right parenthesis � 1200 x over denominator x left parenthesis x plus 100 right parenthesis end fraction equals 1
fraction numerator 1200 x plus 120000 � 1200 x over denominator x squared plus 100 x end fraction equals 1
120000 space equals space x squared space plus space 100 x space space x squared space plus space 100 x space � space 120000 space equals space 0 space space x squared space � space 300 x space plus space 400 x space � space 120000 space equals space 0 space x left parenthesis x space � space 300 right parenthesis space plus space 400 left parenthesis x space � space 300 right parenthesis space equals space 0 space space x space equals space 300 space space o r space space x space equals space � space 400

Since, the speed of the aeroplane can never be negative

Hence, the usual speed of aeroplane is 300 km/hr


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