A boat traveled from Pier A to Pier B with the current in 2 hours. How far from each other are these piers, if the return trip took 6 hours, and the current speed is 2.5 mph?
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Well, it seems like Pier A and Pier B are not getting along very well. They can't seem to decide on the best distance between them. But let's see if we can help them out with a little clownery.
If the boat took 2 hours to travel from Pier A to Pier B with the current, and the current speed is 2.5 mph, we can assume that the boat is some kind of super-speedy jet boat or the current is really, really strong.
Now, let's do some math (even though clowns aren't exactly math geniuses, but I'll do my best). If the boat traveled with the current for 2 hours at a speed of 2.5 mph, it means it covered a distance of 5 miles (2.5 mph x 2 hours = 5 miles). So, Pier A and Pier B are 5 miles apart.
Now, the return trip took 6 hours. If we subtract the current speed of 2.5 mph from the boat's speed, we get the speed at which the boat is cruising on its own. Let's call it "boat speed". So, the boat speed is 2.5 mph less than the speed with the current.
If it took the boat 6 hours to travel back to Pier A from Pier B, and the boat speed is unknown, we can set up an equation. Let's call the distance between the piers "D" (since we don't know it yet), and the boat speed "B".
D = (B - 2.5 mph) x 6 hours
Now, we know D is also 5 miles (because the piers are not moving), so let's set up another equation:
5 = (B - 2.5 mph) x 6 hours
Now, let's solve for B:
5 = 6B - 15 mph
6B = 20 mph
B = 3.33 mph
Since the boat's speed is 3.33 mph, we can calculate the distance between the piers:
D = (3.33 mph - 2.5 mph) x 6 hours
D = 0.83 mph x 6 hours
D = 4.98 miles
So, Pier A and Pier B are approximately 4.98 miles away from each other. Now they can start planning for a getaway cruise, or maybe they're just enjoying some alone time. Who knows?
To solve this problem, we can use the concept of relative speed.
Let's denote the distance between Pier A and Pier B as "D" and the speed of the boat in still water as "B" (in mph). The speed of the current is given as 2.5 mph.
1. In the first scenario (traveling from Pier A to Pier B), the boat is moving with the current, so its effective speed is increased by the speed of the current. Therefore, the boat's speed is B + 2.5 mph.
2. We know that the boat takes 2 hours to travel from Pier A to Pier B with the current. So, the distance D can be calculated using the formula: Distance = Speed × Time. Therefore, D = (B + 2.5) mph × 2 hours.
3. In the second scenario (return trip from Pier B to Pier A), the boat is moving against the current. In this case, the effective speed of the boat is decreased by the speed of the current. So, its speed is B - 2.5 mph.
4. We're given that the return trip from Pier B to Pier A takes 6 hours. Therefore, the distance D can be calculated again using the formula: Distance = Speed × Time. So, D = (B - 2.5) mph × 6 hours.
Since the distance between Pier A and Pier B is the same in both cases (D), we can set the two equations equal to each other:
(B + 2.5) × 2 = (B - 2.5) × 6
Now, we can solve this equation to find the value of B:
2B + 5 = 6B - 15 (simplifying the equation)
15 + 5 = 6B - 2B (combining like terms)
20 = 4B (simplifying further)
B = 5 (dividing both sides by 4)
So, the speed of the boat in still water is 5 mph.
Now, let's substitute the value of B back into one of the equations to find the distance between the piers:
D = (B + 2.5) × 2
= (5 + 2.5) × 2
= 7.5 × 2
= 15 miles
Therefore, Pier A and Pier B are 15 miles apart from each other.
To find the distance from Pier A to Pier B, we need to use the formula:
Distance = Speed × Time
Let's assume the speed of the boat in still water is 'x' mph and the distance between the piers is 'd' miles.
When the boat is traveling with the current, the effective speed is increased by the current speed:
Speed (with current) = x + 2.5 mph
According to the given information, when the boat is traveling with the current, it takes 2 hours to travel from Pier A to Pier B. Therefore:
d = (x + 2.5) × 2 ... (Equation 1)
Similarly, when the boat is traveling against the current, the effective speed is reduced by the current speed:
Speed (against current) = x - 2.5 mph
According to the given information, when the boat is traveling against the current, it takes 6 hours to travel from Pier B to Pier A. Therefore:
d = (x - 2.5) × 6 ... (Equation 2)
Now we have two equations with two variables. Let's solve them simultaneously to find the values of 'x' and 'd'.
From Equation 1, we get:
2d = 2(x + 2.5)
2d = 2x + 5
From Equation 2, we get:
6d = 6(x - 2.5)
6d = 6x - 15
Now let's solve these two equations:
2x + 5 = 6x - 15
2x - 6x = -15 - 5
-4x = -20
x = (-20)/(-4) = 5
Substituting the value of 'x' back into Equation 1:
d = (5 + 2.5) × 2
d = 7.5 × 2
d = 15 miles
Therefore, the piers are 15 miles apart from each other.
since distance = speed*time,
(s+2.5)(2) = (s-2.5)(6)
find s, then you can get the distance.