Assuming that the petrol burnt per hour 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/hour is `(3c)/(2)` km/hour.

The cost of fuel for running a bus is proportional to the square of the speed generated in km/h. It cost Rs 48 per hour when the bus is moving with a speed of 20 km/h. What is the most economical speed if the fixed charges are Rs 108 for one hour, over and above the running charges?

A motor boat whose speed is 18 km/hr in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

The ratio of speeds of two vehicles is 2:3.If the first vehicle covers 50 km in 3 hours what distance would the second vehicle cover in 2 hours?

A car takes 2 hours to reach a destination by travelling at the speed of 60 km/h. How long will it take when the car travels at the speed of 80 km/h?

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour ?

A train travels between two stations ambala and Amritsar. While goind from Ambala to Amritsar, it takes 3 hours and its average speed is 100km/hr. when coming back from Amritsar of Ambala, it takes 2 hours and it average speed is 150 km/hr. obtain the average speed during the whole journey?

A furniture firm manufactures chairs and tables, each requiring the use of three machines A, B and C. Production of one chair requires 2 hours on machine A, 1 hour on machine B and 1 hour on machine C. Each table requires 1 hour each on machine A and B and 3 hours on machine C. The profit obtained by selling on chair is ₹ 30 while by selling one table the profit is ₹ 60. The total time available per week on machine A is 70 hours, on machine B is 40 hours and on machine C is 90 hours. How many chairs and tables should be made per week so as to maximize profit ? Formulate the problem as L.P.P. and sovle it graphically.

On complete combustion a litre of petrol gives off heat equivalent to 3 xx 10^7 J . In a test drive a car weighing 1200 kg, including the mass of driver, runs 15 km per litre while moving with a uniform speed on a straight track. Assuming tha friction offered by the road surface and air to be uniform, calcuate the force of friciton acting on the car during the test drive, if the efficiency of the car engine were 0.5.