Assuming the petrol burnt per hours in driving a motor boat varies as the cube of its velocity, show that the most economical speed when going against a current of c km per hour is `(3c )/(2)` km per hour.

The cost of fuel of an engine varies as the square of its velocity and the cost of fuel is ₹ 48 per hour when the velocity is 16 km per hour. If other expenses be ₹ 300 per hour, then show that the most economical velocity for a journey of a given distance is 40 km per hour.

Find the distance covered by a car in 2(2/5) hours at a speed of 46(2/3) km per hour.

A locomotive engine without wagons can go 35 km per hour and its speed is diaminished by a quantity which varies as the square root of the number of wagons attached , with 9 wagons its speed is 20 km per hour . Find the least number of wagons which the engine can move.

Calculate the wavelength of 1000 kg rocket moving with a velocity of 300 km per hour.

A man has to spend Rs.16 per km on petrol if he rides his motor-car at 30 km per hour and the cost on petrol rises to Rs.20 per km if he rides his car at 45 km per hour. He has Rs.200 to spend on petrol and desires to travel maximum distance within 2 hours. Formulate the given data in the form of inequations and show graphically the region representing the solution of the inequations.

A boat travels 64 km in 16 hours in favor of the current and 24 km in 8 hours against the current of the river. Find the velocity of the boat in steady water and the velocity of the current with the help of graph.

An automobile driver travels from a plain to a hill station 120 km away at an average speed of 30 km per hour. He then makes the return trip at an average speed 25 km per hour. He covers another 120 km on the plain at an average speed of 50 km per hour. His average speed (in km/hr) over the entire distance of 360 km will be