# math

A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake. She can bicycle at the rate of 6 mi/h and row a boat at 3 mi/h. What is the shortest amount of time she can travel to point C?

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1. Take a look here:

math.stackexchange.com/questions/839014/optimization-problem-not-sure-how-to-proceed

1. 👍
2. 👎
2. Boat: V * t = 4 mi.
t = 4/V = 4/3 = 1.33 h.

Bicycle: The distance is 1/2 circle.
d = pi * 2r/2 = pi * r = 3.14 * 2 = 6.28 mi.
V * t = 6.28.
t = 6.28/V = 6.28/6 = 1.05 h. = Shortest time.

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2. 👎

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The text passage contains a mathematical question and an answer to that question. The question is about finding the shortest amount of time a woman can travel to a point C, which is diametrically opposite to point A on a circular lake, given her rowing and bicycling speeds. The answer provided calculates the time for both rowing and bicycling and concludes that bicycling is the shortest time.

Content structure: The passage starts with a word problem, followed by a reference to a solution on an external website, and then provides a detailed solution to the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# math

A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C diametrically opposite A on the other side of the lake. She can bicycle at the rate of 6 mi/h and row a boat at 3 mi/h. What is the shortest amount of time she can travel to point C?

1. 👍
2. 👎
3. 👁
1. Take a look here:

math.stackexchange.com/questions/839014/optimization-problem-not-sure-how-to-proceed

1. 👍
2. 👎
2. Boat: V * t = 4 mi.
t = 4/V = 4/3 = 1.33 h.

Bicycle: The distance is 1/2 circle.
d = pi * 2r/2 = pi * r = 3.14 * 2 = 6.28 mi.
V * t = 6.28.
t = 6.28/V = 6.28/6 = 1.05 h. = Shortest time.

1. 👍
2. 👎

## Similar Questions

1. ### physics

A Ferris wheel with radius 14.0 m is turning about a horizontal axis through its center as shown in the figure. The linear speed of a passenger on the rim is constant and equal to 7.0 m/s. What are the magnitude and direction of

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A woman at a point A on the shore of a circular lake with radius r=4 wants to arrive at the point C diametrically opposite A on the other side of the lake in the shortest possible time. She can walk at the rate of 10mph and row a

3. ### Physic

A river 1.00 mile wide flows with a constant speed of 1.00 mi/h. A woman leaves from a point on the river bank. The woman rows a boat 1.00 mi directly upstream and returns to the starting point. Her speed in still water is 2.00

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To get off a frozen frictionless lake, a 70.0 kg person takes off a 0.150 kg shoe and throws it horizontally directly away from the shore with a speed of 2.00 m/s. If the perrson is 5.00 m from the shore, how long does it take for

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The ship in Figure P14.35 travels along a straight line parallel to the shore and a distance d = 500 m from it. The ship’s radio receives simultaneous signals of the same frequency from antennas A and B, separated by a distance

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Which statement best describes the conclusion and its likely effect on readers? Jake wrote a story about a woman who goes sailing alone for the first time after taking sailing lessons. The woman needs to sail a small sailboat to

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The shoreline of a lake is a circle with diameter 3 km. Peter stands at point E and wants to reach the diametrically opposite point W. He intends to jog along the north shore to a point P and then swim the straight line distance

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One afternoon, a couple walks three-fourths of the way around a circular lake, the radius of which is 1.03 km. They start at the west side of the lake and head due south to begin with. (a) What is the distance they travel? (b)

1. ### Calculus Minima Problems

A small island is 2 km off shore in a large lake .A woman on the island can row her boat 10 km/hr and can run at a speed of 20 km/hr. If she rows to the closest point of the straight shore, she will land 6 km from a village on the

2. ### Calculus

A lighthouse stands 450 m off a straight shore and the focused beam of its light revolves four times each minute. As shown in the​ figure, P is the point on shore closest to the lighthouse and Q is a point on the shore 250 m

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Jim paddles from one shore of a lake three miles wide at 4 mph, and John paddles from the opposite shore at 5 mph. How long will they travel before they meet? please explain to me
user
The text passage contains a mathematical question and an answer to that question. The question is about finding the shortest amount of time a woman can travel to a point C, which is diametrically opposite to point A on a circular lake, given her rowing and bicycling speeds. The answer provided calculates the time for both rowing and bicycling and concludes that bicycling is the shortest time.

Content structure: The passage starts with a word problem, followed by a reference to a solution on an external website, and then provides a detailed solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER