A boat's crew rowed 13.5 miles downstream, with the current, in 1.5 hours. The return trip upstream against the current covered the same distance, but took 4.5 hours. Find the crew's rowing rate in still water and the rate of the current.
6 miles per hour still water
The current flow 3 miles per hour
To find the crew's rowing rate in still water, let's call it "x", and the rate of the current, let's call it "y".
We can start by setting up a system of equations based on the given information:
(1) (x + y) * 1.5 = 13.5
(2) (x - y) * 4.5 = 13.5
Equation (1) represents the downstream trip, where the boat speed is the rowing rate in still water (x) plus the rate of the current (y), multiplied by the time it took (1.5), which equals the distance of 13.5 miles.
Equation (2) represents the upstream trip, where the boat speed is the rowing rate in still water (x) minus the rate of the current (y), multiplied by the time it took (4.5), which again equals the distance of 13.5 miles.
Now, let's solve this system of equations to find the values of x and y.
Start by simplifying equation (1):
1.5x + 1.5y = 13.5 (divide both sides by 1.5)
This simplifies to:
x + y = 9 (equation 3)
Now, let's simplify equation (2):
4.5x - 4.5y = 13.5 (divide both sides by 4.5)
This simplifies to:
x - y = 3 (equation 4)
Now, we can solve equations 3 and 4 simultaneously.
First, let's solve equation 3 for x:
x = 9 - y
Next, substitute this value of x into equation 4:
(9 - y) - y = 3
Simplify the equation:
9 - 2y = 3
Move the constant to the right side:
-2y = 3 - 9
-2y = -6
Now, divide both sides by -2 to solve for y:
y = -6 / -2
y = 3
Now that we have the value of y, we can substitute it back into equation 3 to solve for x:
x + 3 = 9
Subtract 3 from both sides:
x = 6
Therefore, the crew's rowing rate in still water is 6 miles per hour, and the rate of the current is 3 miles per hour.