The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15k...

The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15km. how far would the vehicle go on 9 litres of petrol?

Answer Details

Since the rate of consumption of petrol varies directly as the square of the distance covered, let's assume that the rate is k\(\frac{\text{litres}}{\text{km}^2}\). Then we can write the relationship as: rate of consumption = k(distance covered)\(^2\) We are given that when the distance covered is 15 km, the rate of consumption is 4 litres. Substituting these values in the above equation, we get: 4 = k(15)\(^2\) k = \(\frac{4}{15^2}\) Now, we need to find how far the vehicle can go on 9 litres of petrol. Let's assume that the vehicle can travel a distance of x km on 9 litres of petrol. Using the same equation as before, we get: 9 = \(\frac{4}{15^2}\)(x)\(^2\) Simplifying this equation, we get: x\(^2\) = \(\frac{9}{\frac{4}{15^2}}\) x\(^2\) = 506.25 x = 22.5 Therefore, the vehicle can travel 22.5 km on 9 litres of petrol. So the answer is 22\(\frac{1}{2}\)km.