Question

Homework: Homework 8 - Chapter 7 (Sections 7.2 and 7.3) and Score: 0 of 7 pts 12 of 21 (10 complete) Text Problem 3.3 Robert has entered a competition in which he must drive from his home town of Paris to London, a distance of approximately 450 km. If he arrives in 5 hours (an average speed of 90 km/h), he will receive a prize of €300 - 6 hours (an average speed of 75 km/h), he receives €270 As per the competition rules, he must pay for his own gasoline. Robert has calculated that he will average • 20 km per liter at 90 km/h • 25 km per liter at 75 km/h Assume that the price of gasoline is 63 per liter. To maximize his winnings (prize money minus the cost of gasoline), Robert must drive at a speed of km/h (Enter your response as an integer) Enter your answer in the answer box and then click Check Answer. 3 parts remaining

Answer 1

At 90 km/h , the trade off is

Cost of gasoline =$3 per litre

He covers a distance 20 km from 1 litre of gasoline

Therefore to cover 450 km her will need 450/20 = 22.5 litre of gasoline which is equal to $ 22.5*3 = $67.5

He earns $300

In total he would profit = $300-67.5 = $232.5

Similarly

At 75 km/h , the trade off is

Cost of gasoline =$3 per litre

He covers a distance 25 km burning 1 litre of gasoline

Therefore to cover 450 km her will need 450/25 = 18 litre of gasoline which is equal to $ 18*3 = $54

He earns $270

In total he would profit = $(270-54 ) = $216

232.5>216

Robert must drive at a speed of 90km/h