A passenger boat which travels 6 mph faster than a freighter required 3 days less time to make a trip of 2592 miles. Find the rate of the passenger boat.

rate of passenger boat --- x mph

rate of freighter --------- x-6 mph

2592/(x-6) - 2592/x = 72 , assuming they travel 24 hours per day

multiply each term by x(x-6)

2592x - 2592(x-6) = 72x(x-6)
2592x - 2592x + 15552 = 72x^2 - 432x

72x^2 - 432x - 15552 = 0
9x^2 - 54x - 1944= 0
(x - 18)(9x + 108) = 0
x = 18 or x is a negative

the rate of the passenger boat was 18 mph
the rate of the freighter was 12 mph

check
2592/18 = 144 hrs
2592/12 = 216441 hrs
difference is 216-144 = 72
My answer of x = 18 is correct

To solve this problem, we can set up two equations based on the given information:

Let's assume the rate of the freighter (slower boat) is represented by 'x' miles per hour.

1. Distance equation:
The distance traveled by both the passenger boat and the freighter is given as 2592 miles.
Therefore, the time taken by the passenger boat (faster boat) is 3 days less than the time taken by the freighter.

Let's say the time taken by the freighter is 't' hours. So, the time taken by the passenger boat is 't-3' hours.

Based on the formula: Distance = Rate * Time, we can write the equation for the faster boat (passenger boat) as:
2592 = (x+6) * (t-3)

2. Rate equation:
The rate of the passenger boat is given as 6 mph faster than the freighter, so we can represent it as 'x+6'.

Now, we have two equations:
2592 = (x+6) * (t-3) -- Equation 1
x = rate of the freighter -- Equation 2

To find the rate of the passenger boat (x+6), we need to solve these equations simultaneously.

To solve Equation 1, you need to know the value of 't', which represents the time taken by the freighter. Unfortunately, this value is not given in the question. Please provide the value of 't', so we can proceed to find the rate of the passenger boat.