If a young man rides his motorcycle at 40 km per hour, he has to spend 6 per km on petrol and if he rides it at 50 km hour, the petrol cost rises to 10 per km. He has 500 to spend on petrol and wishes to find the maximum distance he can travel within one hour. Formulate the data in the form of inequation and draw a graph representing the solution of these inequations.

Let the distance covered with speed 40 km/hr = x km


And the distance covered with speed 50 km/hr = y km


We know that,



Therefore , maximum speed covered within one hour is



Thus , according to equation ,


Maximum speed covered ,


Subject to the constraint ,





Now plotting both the line on graph paper , we have ,



Distance covered with speed 40 km/hr = x = 0


Distance covered with speed 50 km/hr = y = 50


Therefore , maximum distance covered = 0 + 50 = 50 km


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