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Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?
  • a)
    (x + y) / t
  • b)
    2(x + t) / xy
  • c)
    2xyt / (x + y)
  • d)
    2(x + y + t) / xy
  • e)
    x(y + t) + y(x + t)
Correct answer is option 'C'. Can you explain this answer?
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Bob bikes to school every day at a steady rate of x miles per hour. On...
Let b be the number of hours Bob spends biking. Then (t – b) is the number of hours he spends walking. Let d be the distance in miles from his home to school. Since he had the flat tire halfway to school, he biked d/2 miles and he walked d/2 miles. Now we can set up the equations using the formula rate x time = distance. Remember that we want to solve for d, the total distance from Bob's home to school.
1) xb = d/2
2) y(t – b) = d/2
Solving equation 1) for b gives us:
3) b = d/2x                 Substituting this value of b into equation 2 gives:
4) y(t – d/2x) = d/2    Multiply both sides by 2x:
5) 2xy(t – d/2x) = dx  Distribute the 2xy
6) 2xyt – dy = dx       Add dy to both sides to collect the d's on one side.
7) 2xyt = dx + dy       Factor out the d
8) 2xyt = d(x + y)      Divide both sides by (x + y) to solve for d
9) 2xyt / (x + y) = d
The correct answer is C.
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Bob bikes to school every day at a steady rate of x miles per hour. On...
Solution:

Given: Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home.

To Find: How many miles is it from the school to Bob's home?

Assumption: Let the distance between his home and school be d miles.

Distance covered while biking: Since he bikes to school every day at a steady rate of x miles per hour, he would have covered d/2 miles in t/2 hours when he had a flat tire.

Distance covered while walking: After he had a flat tire, he immediately started walking to school at a steady pace of y miles per hour. So, he would have covered another d/2 miles in t/2 hours.

Total distance covered: The total distance covered by Bob to reach the school is the sum of the distance covered while biking and while walking, which is d miles.

Formula: The formula to calculate distance is given as distance = speed x time

Calculation: Using the above formula we can express the distance as:

d = x(t/2) + y(t/2)

Solving for d, we get:

d = 2xyt/(x+y)

Hence, the correct answer is option (c) 2xyt / (x + y).
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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.Given the information in the passage, Sommerer and Ott are most likely to agree with which one of the following?

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Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?a)(x + y) / tb)2(x + t) / xyc)2xyt / (x + y)d)2(x + y + t) / xye)x(y + t) + y(x + t)Correct answer is option 'C'. Can you explain this answer?
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Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?a)(x + y) / tb)2(x + t) / xyc)2xyt / (x + y)d)2(x + y + t) / xye)x(y + t) + y(x + t)Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?a)(x + y) / tb)2(x + t) / xyc)2xyt / (x + y)d)2(x + y + t) / xye)x(y + t) + y(x + t)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob's home?a)(x + y) / tb)2(x + t) / xyc)2xyt / (x + y)d)2(x + y + t) / xye)x(y + t) + y(x + t)Correct answer is option 'C'. Can you explain this answer?.
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