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A speed boat travels at a speed of x miles per hour in still water. With a favourable current, the speed boat travels downstream and reaches its destination in 2.5 hours. The speedboat travels back upstream against the current and covers the same distance in 3.5 hours.  If the speed of the current is 1mph, then what is the value of x?
  • a)
    2.5
  • b)
    3.5
  • c)
    4
  • d)
    6
  • e)
    9
Correct answer is option 'D'. Can you explain this answer?
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A speed boat travels at a speed of x miles per hour in still water. Wi...
Given:

- Speed of boat in still water = x mph
- Speed of current = 1 mph
- Time taken downstream = 2.5 hours
- Time taken upstream = 3.5 hours

To find: Speed of boat in still water (x)

Concepts used:

- Speed = Distance/Time
- Let distance be D
- Downstream speed = (x+1) mph
- Upstream speed = (x-1) mph
- Distance downstream = Distance upstream

Solution:

Let distance be D.

Downstream:

- Speed of boat = (x+1) mph
- Time taken = 2.5 hours
- Distance = Speed x Time = (x+1) x 2.5 = 2.5x + 2.5

Upstream:

- Speed of boat = (x-1) mph
- Time taken = 3.5 hours
- Distance = Speed x Time = (x-1) x 3.5 = 3.5x - 3.5

Since distance downstream = distance upstream, we can equate the two expressions:

2.5x + 2.5 = 3.5x - 3.5

Simplifying, we get:

6 = x

Therefore, the speed of the boat in still water is 6 mph.

Answer: Option D.
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Community Answer
A speed boat travels at a speed of x miles per hour in still water. Wi...
Solution:
  • Let the speed of the boat in still water be x mph and the speed of the current be 1 mph.
  • When the boat travels downstream with the current, the effective speed is (x + 1) mph. The time taken to reach the destination is 2.5 hours.
  • When the boat travels upstream against the current, the effective speed is (x - 1) mph. The time taken to cover the same distance is 3.5 hours.
We can use the formula: Distance = Speed * Time
  • Distance downstream = (x + 1) * 2.5 = 2.5x + 2.5
  • Distance upstream = (x - 1) * 3.5 = 3.5x - 3.5
  • Since the distances covered in both directions are the same, we can equate the two expressions:
    2.5x + 2.5 = 3.5x - 3.5
Solving for x:
2.5 + 3.5 = 3.5x - 2.5x
6 = 1.0x
x = 6
Therefore, the speed of the boat in still water is 6 mph, which corresponds to option D.
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One of the foundations of scientific research is that an experimental result is credible only if it can be replicated—only if performing the experiment a second time leads to the same result. But physicists John Sommerer and Edward Ott have conceived of a physical system in which even the least change in the starting conditions—no matter how small, inadvertent, or undetectable—can alter results radically. The system is represented by a computer model of a mathematical equation describing the motion of a particle placed in a particular type of force field.Sommerer and Ott based their system on an analogy with the phenomena known as riddled basins of attraction. If two bodies of water bound a large landmass and water is spilled somewhere on the land, the water will eventually make its way to one or the other body of water, its destination depending on such factors as where the water is spilled and the geographic features that shape the water’s path and velocity. The basin of attraction for a body of water is the area of land that, whenever water is spilled on it, always directs the spilled water to that body.In some geographical formations it is sometimes impossible to predict, not only the exact destination of the spilled water, but even which body of water it will end up in. This is because the boundary between one basin of attraction and another is riddled with fractal properties; in other words, the boundary is permeated by an extraordinarily high number of physical irregularities such as notches or zigzags. Along such a boundary, the only way to determine where spilled water will flow at any given point is actually to spill it and observe its motion; spilling the water at any immediately adjacent point could give the water an entirely different path, velocity, or destination.In the system posited by the two physicists, this boundary expands to include the whole system: i.e., the entire force field is riddled with fractal properties, and it is impossible to predict even the general destination of the particle given its starting point. Sommerer and Ott make a distinction between this type of uncertainty and that known as “chaos”; under chaos, a particle’s general destination would be predictable but its path and exact destination would not.There are presumably other such systems because the equation the physicists used to construct the computer model was literally the first one they attempted, and the likelihood that they chose the only equation that would lead to an unstable system is small. If other such systems do exist, metaphorical examples of riddled basins of attraction may abound in the failed attempts of scientists to replicate previous experimental results—in which case, scientists would be forced to question one of the basic principles that guide their work.According to the passage, Sommerer and Ott’s model differs from a riddled basin of attraction in which one of the following ways?

One of the foundations of scientific research is that an experimental result is credible only if it can be replicated—only if performing the experiment a second time leads to the same result. But physicists John Sommerer and Edward Ott have conceived of a physical system in which even the least change in the starting conditions—no matter how small, inadvertent, or undetectable—can alter results radically. The system is represented by a computer model of a mathematical equation describing the motion of a particle placed in a particular type of force field.Sommerer and Ott based their system on an analogy with the phenomena known as riddled basins of attraction. If two bodies of water bound a large landmass and water is spilled somewhere on the land, the water will eventually make its way to one or the other body of water, its destination depending on such factors as where the water is spilled and the geographic features that shape the water’s path and velocity. The basin of attraction for a body of water is the area of land that, whenever water is spilled on it, always directs the spilled water to that body.In some geographical formations it is sometimes impossible to predict, not only the exact destination of the spilled water, but even which body of water it will end up in. This is because the boundary between one basin of attraction and another is riddled with fractal properties; in other words, the boundary is permeated by an extraordinarily high number of physical irregularities such as notches or zigzags. Along such a boundary, the only way to determine where spilled water will flow at any given point is actually to spill it and observe its motion; spilling the water at any immediately adjacent point could give the water an entirely different path, velocity, or destination.In the system posited by the two physicists, this boundary expands to include the whole system: i.e., the entire force field is riddled with fractal properties, and it is impossible to predict even the general destination of the particle given its starting point. Sommerer and Ott make a distinction between this type of uncertainty and that known as “chaos”; under chaos, a particle’s general destination would be predictable but its path and exact destination would not.There are presumably other such systems because the equation the physicists used to construct the computer model was literally the first one they attempted, and the likelihood that they chose the only equation that would lead to an unstable system is small. If other such systems do exist, metaphorical examples of riddled basins of attraction may abound in the failed attempts of scientists to replicate previous experimental results—in which case, scientists would be forced to question one of the basic principles that guide their work.Given the information in the passage, Sommerer and Ott are most likely to agree with which one of the following?

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A speed boat travels at a speed of x miles per hour in still water. With a favourable current, the speed boat travels downstream and reaches its destination in 2.5 hours. The speedboat travels back upstream against the current and covers the same distance in 3.5 hours. If the speed of the current is 1mph, then what is the value of x?a)2.5b)3.5c)4d)6e)9Correct answer is option 'D'. Can you explain this answer?
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