It is a beautiful spring day so you decide to go rowing upstream on your favorite river. You row at a constant rate of 1 mile per hour. Suddenly a gust of wind blows your hat off into the water. You watch it float away downstream but since you never really liked it that much, you continue to row upstream for 10 minutes. Wait! You just remember that you had tucked your concert tickets in the hat! Quickly, you turn around and row downstream at the same rate looking for the hat. You finally catch up to it at the same place that you started out from, and rescue your tickets.

Question

It is a beautiful spring day so you decide to go rowing upstream on your favorite river. You row at a constant rate of 1 mile per hour. Suddenly a gust of wind blows your hat off into the water. You watch it float away downstream but since you never really liked it that much, you continue to row upstream for 10 minutes. Wait! You just remember that you had tucked your concert tickets in the hat! Quickly, you turn around and row downstream at the same rate looking for the hat. You finally catch up to it at the same place that you started out from, and rescue your tickets.

What is the speed of the current?

Answer 1

To determine the speed of the current, we need to analyze the information provided in the problem. Let's break it down step by step:

1. The rower is rowing upstream at a constant rate of 1 mile per hour.
2. The hat floats downstream due to the wind.
3. The rower continues rowing upstream for 10 minutes before turning around.
4. The rower rows downstream at the same rate to catch up to the hat.

To solve this problem, we can consider the relationship between the rower's speed and the speed of the current.

Let's assume "x" represents the speed of the current in miles per hour.

When rowing upstream:
Rowing speed - Current speed = 1 mile per hour - x miles per hour

When rowing downstream:
Rowing speed + Current speed = 1 mile per hour + x miles per hour

Since the rower turns around and catches up to the hat at the same place where they started, the distance covered in both directions must be the same. We can calculate the distance traveled in 10 minutes (1/6 hour) when rowing upstream and downstream based on their respective speeds.

Distance traveled upstream: (1 mile per hour - x miles per hour) * (1/6 hour)
Distance traveled downstream: (1 mile per hour + x miles per hour) * (1/6 hour)

As the distance traveled upstream and downstream is the same, we can equate the two equations:

(1 mile per hour - x miles per hour) * (1/6 hour) = (1 mile per hour + x miles per hour) * (1/6 hour)

Now, let's solve for "x" to find the speed of the current:

1/6 - (x/6) = 1/6 + (x/6)
1/6 - x/6 = 1/6 + x/6
1 - x = 1 + x

Now, we can simplify the equation:

-2x = 0
x = 0

According to the calculations, the speed of the current is 0 miles per hour.