A cruise ship made a trip of 198 mi in 9 h. The ship traveled the first 54 mi at a constant rate before increasing its speed by 6 mph. Then it traveled another 144 mi at the increased speed. Find the rate of the cruise ship for the first 54 mi.

Question

Quizplus · Accepted Answer

Let the initial speed of the cruise ship be $x$ mph. For the first 54 miles, the speed is $x$ mph, and for the remaining 144 miles, the speed is $x + 6$ mph. The total time taken for the trip is 9 hours. We can set up the equation based on the time taken for each part of the trip:$$\frac{54}{x} + \frac{144}{x + 6} = 9$$Multiplying through by $x(x + 6)$ to clear the denominators gives:$$54(x + 6) + 144x = 9x(x + 6)$$Expanding and simplifying:$$54x + 324 + 144x = 9x^2 + 54x$$Combining like terms and moving everything to one side gives a quadratic equation:$$9x^2 - 144x - 324 = 0$$Dividing the entire equation by 9 to simplify:$$x^2 - 16x - 36 = 0$$Factoring or using the quadratic formula, we find that $x = 18$ or $x = -2$. Since speed cannot be negative, $x = 18$ mph is the correct answer.

A Cruise Ship Made a Trip of 198 Mi in 9