A penguin swimming with the ocean current in search of food takes 1 hour to travel 9 miles. Its return trip upstream to its starting point takes it 3 hours, What is the penguin's speed in still water?
Thanks.
distance = speed/time
To find the penguin's speed in still water, we need to consider the concept of relative speed.
Let's assume that the speed of the ocean current is C and the speed of the penguin in still water is P.
When the penguin is swimming downstream with the ocean current, its actual speed will be the sum of its speed in still water and the speed of the current. So, the penguin's speed downstream is P + C.
Given that it takes 1 hour for the penguin to swim 9 miles downstream, we can set up the equation:
(P + C) * 1 = 9 (Equation 1)
When the penguin is swimming upstream against the current, its actual speed will be the difference between its speed in still water and the speed of the current. So, the penguin's speed upstream is P - C.
Given that it takes 3 hours for the penguin to swim back 9 miles upstream to its starting point, we can set up another equation:
(P - C) * 3 = 9 (Equation 2)
Now, we need to solve this system of equations to find the values of P and C.
From Equation 1, we can rewrite it as:
P + C = 9 (Equation 3)
From Equation 2, we can rewrite it as:
3P - 3C = 9 (Equation 4)
We can simplify Equation 4 by dividing both sides by 3:
P - C = 3 (Equation 5)
Now we have a system of two equations:
P + C = 9 (Equation 3)
P - C = 3 (Equation 5)
We can solve this system of equations by adding Equation 3 and Equation 5:
(P + C) + (P - C) = 9 + 3
This simplifies to:
2P = 12
Divide both sides by 2:
P = 6
Therefore, the penguin's speed in still water is 6 miles per hour.