Question

A horse can pull an empty cart at the speed of 18km per hour and the reduction in its speed is directly proportional to the square root of the number of boxes it can carry of equal weight of 10kg each. If the speed of the cart is 12km per hour when 9 boxes are loaded in the cart, find the maximum weight that can be carried if the speed of the cart is to be maintained at least 10km per hour.

Answer 1

Answer:

160 kg

Step-by-step explanation:

Speed of cart ∝ √number of boxes

Speed of cart = ( k × √number of boxes  ) + c

Where k & c are constants

When number of boxes = 0

Speed of cart = (k × 0) + c

=> 18 = c

Speed of cart = 12 km/Hr when 9 boxes

=> 12 = k √9 + 18

=> -6 = 3k

=> k = -2

Speed of cart = (-2 × √Number of boxes ) + 18

Speed to be maintained at 10 km/Hr

10 = -2 × √Number of boxes + 18

=> -8 = -2 × √Number of boxes

=> 4 = √Number of boxes

Squaring both sides

16 = Number of Boxes

So it can carry 16 number of boxes

Each box weigh = 10 kg

Total weight = 16 × 10 = 160 kg