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Question

A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600km away in time, it had to increase its speed by 400km/hr from its usual speed. Find the usual speed of the plane.

 


Solution

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

Then the increased speed  of the plane is = (x + 4000) km/hr

Time taken by the plane under usual speed  to cover  1600km = 1600 over xhr

Time taken by the plane under increased speed  to cover 1600 km = 1600/(x + 400)hr

Therefore,
1600 over x � fraction numerator 1600 over denominator left parenthesis x plus 400 right parenthesis end fraction equals 40 over 60
fraction numerator 1600 left parenthesis x plus 400 right parenthesis � 1600 x over denominator x left parenthesis x plus 400 right parenthesis end fraction equals 2 over 3
fraction numerator 1600 x plus 640000 � 1600 x over denominator x squared plus 400 x end fraction equals 2 over 3
1920000 space equals space 2 x squared space plus space 800 x space space 2 x squared space plus space 800 x space � space 1920000 space equals space 0 space space 2 left parenthesis x squared space plus space 400 x space � space 960000 right parenthesis space equals space 0 space space x squared space plus space 400 x space � space 960000 space equals space 0 space space x squared space � space 800 x space plus space 1200 x space � space 960000 space equals space 0 space space x left parenthesis x space � space 800 right parenthesis space plus space 1200 left parenthesis x space � space 800 right parenthesis space equals space 0 space space left parenthesis x space � space 800 right parenthesis left parenthesis x space plus space 1200 right parenthesis space equals space 0 space space x space space equals space 800 space space o r space x space equals space minus 1200

Since the speed of the train can never be negative

Therefore, the usual speed of the train is 800 km/hr.

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