A boat can maintain a constant speed of 34 mph relative to the water. The boat makes a trip upstream to a certain point in 21 minutes; the return trip takes 13 minutes. What is the speed of the current?
To find the speed of the current, we need to use the concept of relative motion. Let's assume the speed of the boat in still water is 'B' mph and the speed of the current is 'C' mph.
On the upstream trip, the boat is moving against the current, so the effective speed will be reduced. The boat's speed relative to the water will be slower by the speed of the current (B - C). Similarly, on the downstream trip, the boat is moving with the current, so the effective speed will be increased. The boat's speed relative to the water will be faster by the speed of the current (B + C).
Now let's convert the given time durations to hours for convenience. 21 minutes is equal to 21/60 = 0.35 hours, and 13 minutes is equal to 13/60 = 0.22 hours.
For the upstream trip, we have:
Speed of the boat relative to the water = Speed of the boat in still water - Speed of the current
34 mph = B - C
And for the downstream trip, we have:
Speed of the boat relative to the water = Speed of the boat in still water + Speed of the current
34 mph = B + C
We can now solve these two equations to find the values of B and C.
First, let's solve for B by adding the two equations:
34 mph + 34 mph = (B - C) + (B + C)
68 mph = 2B
Dividing both sides by 2, we find:
B = 34 mph
Now, let's substitute the value of B into one of the equations to solve for C. Using the first equation:
34 mph = (34 mph) - C
C = 0 mph
Therefore, the speed of the current is 0 mph.
It is important to note that in this scenario, the speed of the current is zero. This means there is no current affecting the boat's motion.
Distance = rate * time
Let x = speed of current
rate upstream = 34 - x
rate downstream = 34 + x
21(34 - x) = 13(34 + x)
Solve for x.