Question

A truck is to be driven 300 km on a highway at a constant speed of x kmph. Speed rules of the highway required that

30 £ x £ 60. The fuel costs Rs. 10 per litre and is consumed at the rate of 2 + $\frac{x^{2}}{600}$litres per hour. The wages of the driver are Rs. 200 per hour. The most economical speed to drive the truck, in kmph is

• A. 30
• B. 60
• C. 30$\sqrt{3.3}$
• D. 20$\sqrt{3.3}$

Answer 1

Answer: (B)

60

Answer 2

Time taken by the truck = $\frac{300}{x}$hours

\ petrol consumed = $\left( 2 + \frac{x^{2}}{600} \right)\frac{300}{x}$litre

\ expenses on traveling

E = 200 × $\frac{300}{x} + \left( 2 + \frac{x^{2}}{600} \right)\frac{3000}{x}$

=$\frac{60000}{x} + \frac{6000}{x}$+ 5x

= $\frac{66000}{x}$ + 5x

\ $\frac{dE}{dx}$= – $\frac{66000}{x^{2}}$ + 5 < 0 for all x Ī [30, 60]

\ most economical speed is 60 kmph