The speed of a boat in still water is 20 mph. It travels from one pier to another with the current in 4 hours and back against the current in 6 hours and 40 minutes. If the distance between the piers is 100 miles, what is the speed of the current?
Let's assume the speed of the current is x mph.
When the boat is traveling with the current, the effective speed of the boat is 20 + x mph. Given that it takes 4 hours to cover a distance of 100 miles, we can set up the equation as follows:
100 = (20 + x) * 4
Dividing both sides by 4, we have:
25 = 20 + x
Subtracting 20 from both sides, we get:
x = 5 mph
When the boat is traveling against the current, the effective speed of the boat is 20 - x mph. Given that it takes 6 hours and 40 minutes (or 6.67 hours) to cover the same distance of 100 miles, we can set up another equation:
100 = (20 - x) * 6.67
Dividing both sides by 6.67, we have:
x = 20 - (100/6.67)
Simplifying, we get:
x ≈ 20 - 15 ≈ 5 mph
Therefore, the speed of the current is 5 mph.
To find the speed of the current, we can set up a system of equations using the given information.
Let's assume the speed of the current is represented by 'c' mph.
When the boat is traveling with the current, its effective speed would be the sum of the speed of the boat in still water and the speed of the current, i.e., (20 + c) mph.
Similarly, when the boat is traveling against the current, its effective speed would be the difference between the speed of the boat in still water and the speed of the current, i.e., (20 - c) mph.
Now, let's use the formula speed = distance/time to set up the equations:
Equation 1: distance / time = speed
When the boat is traveling with the current:
100 / 4 = 20 + c
Equation 2: distance / time = speed
When the boat is traveling against the current:
100 / (6 + 40/60) = 20 - c
Now, let's solve these equations:
Equation 1: 100 / 4 = 20 + c
25 = 20 + c
c = 25 - 20
c = 5 mph
Equation 2: 100 / (6 + 40/60) = 20 - c
100 / (6 + 2/3) = 20 - c
100 / (20/3) = 20 - c
100 * (3/20) = 20 - c
15 = 20 - c
c = 20 - 15
c = 5 mph
Therefore, the speed of the current is 5 mph.