Answer:
Therefore, the time for the return trip is:
≈ 5.306 seconds
Explanation:
Let's start by finding the speed of the boat. We know that the boat travels 400m at a constant speed, so we can use the formula:
Speed = Distance / Time
Speed = 400m / Time (for one-way trip)
Let's assume that the time for the one-way trip is t. Then we can rewrite the speed formula as:
Speed = 400m / t
Now let's find the time for the return trip. We know that the boat travels the same route at the same speed for 2 minutes, which is equivalent to 120 seconds. This means that the distance traveled on the way back is:
Distance = Speed x Time
Distance = (400m / t) x 120 seconds
Distance = 48000m / t
We also know that when Pilar increases the boat's speed by 10 m/min, the return trip is 60 seconds faster. This means that the time for the return trip is:
t - 60 seconds
Using the same formula as before, the distance traveled on the return trip is:
Distance = (400m / (t + 1/2)) x (t - 60) seconds
Distance = (400m / (t + 1/2)) x (t - 60/60) minutes
Distance = 400m x (t - 60/60) / (t + 1/2) minutes
Now we know that the distance traveled on the way back is equal to the distance traveled on the way there:
48000m / t = 400m x (t - 60/60) / (t + 1/2)
Simplifying this equation, we get:
48 / t = 4 x (t - 1/3) / (t + 1/2)
Multiplying both sides by (t + 1/2), we get:
48(t + 1/2) / t = 4(t - 1/3)
Simplifying this equation, we get:
96 / t = 4t - 4/3
Multiplying both sides by t, we get:
96 = 4t^2 - 4/3t
Multiplying both sides by 3, we get:
288 = 12t^2 - 4t
Rearranging this equation, we get
12t^2 - 4t - 288 = 0
Dividing both sides by 4, we get:
3t^2 - t - 72 = 0
Using the quadratic formula, we can solve for t:
t = [1 ± sqrt(1 + 4(3)(72))] / 6
t = [1 ± sqrt(865)] / 6
Since t must be positive, we take the positive root:
t ≈ 6.366
Therefore, the time for the return trip is:
t - 60 seconds ≈ 6.366 - 60 seconds ≈ 5.306 seconds