A boat crew rowed 20 miles downstream, with the current, covered the same distance, but took 5 hours. Dine the crew's rowing rate in still water and the rate of the current? Still water _ MPH and Current _ MPH.
something is missing here
The current is 2 hours. Sorry about that
To find the crew's rowing rate in still water (still water speed) and the rate of the current, we can set up a system of equations based on the given information.
Let's assume the crew's rowing rate in still water is represented by "x" miles per hour (mph) and the rate of the current is represented by "c" mph.
When rowing downstream with the current, the boat's effective speed is increased by the speed of the current. So, the boat's speed is (x + c) mph. We are also told that the boat covered a distance of 20 miles and it took 5 hours, giving us the equation:
Distance = Speed × Time
20 = (x + c) × 5
Next, when rowing upstream against the current, the boat's effective speed is decreased by the speed of the current. So, the boat's speed is (x - c) mph. We are told that the boat covered the same distance (20 miles) but took an unknown amount of time, which we'll refer to as "t". This gives us another equation:
Distance = Speed × Time
20 = (x - c) × t
Now, we have a system of two equations:
1. 20 = (x + c) × 5
2. 20 = (x - c) × t
To solve this system, we can use the method of substitution.
From equation 1, we can rearrange it to solve for "c" in terms of "x":
20 = 5(x + c)
4 = x + c
c = 4 - x
Now we substitute this expression for "c" into equation 2:
20 = (x - (4 - x)) × t
20 = (2x - 4) × t
20 = 2xt - 4t
Since we don't know the value of "t", we can't find the exact values for "x" and "c". However, we can still find their relationship by eliminating "t".
Divide both sides of the equation by 2t:
10 = xt - 2t
Isolate the "xt" term:
xt = 2t + 10
Divide both sides of the equation by "t":
x = 2 + (10/t)
From this equation, we can see that the still water speed "x" depends on the value of "t". In order to find the specific still water speed and current rate, we need additional information about the time it took when rowing upstream against the current ("t"). Without that, we can only express the relationship between the still water speed and the current rate.