Question

Assume that the distance that a car runs on one liter of petrol varies inversely as the square of the speed at which it is driven. It give a run of 25 kilometer per liter at speed of 30 kilometer per liter. At what speed should it be driven to get a run of 36 kilometer per liter.

Answer 1

mileage of the car = m  km / litre
speed of the car = v km/hr

distance driven = s km        and    amount of petrol = L litres

    mileage is inverse proportional to the square of the speed.
            m  α  1/v²
         m = K / v²,    where K = constant of proportionality , units: km/litre * km²/hr²

   we know,  25 km/litre = K / (30 kmph)²
             K = 25 * 900 = 22,500 km³/litre-hr²

       m = 22, 500 /v²

Now,  v² = K / m = 22, 500 / 36
         v = 150/6 = 25 km/hr

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without finding the constant of proportionality:

   m2 / m1 = v1² / v2²
   m1 = 25 km/litre    v1 = 30 kmph
   v2 = ?    m2 = 36 km/litre

     v2² = m1 v1² / m2 = 25 * 30² / 36 =25 * 25
       v2 = 25 kmph