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 Post subject: GMAT Speed / Distance / TimePosted: Sat Jun 19, 2010 1:53 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
A similar question is here:

-----------

In the figure above, car A and car B travel around a circular park with a radius of 20 miles. Both cars leave from the same point, the START location shown in the figure. Car A travels counter-clockwise at 60 miles/hour and car B travels clockwise at 40 miles/hour. Car B leaves 20 minutes after car A. Approximately how many minutes does it take for the cars to meet after car A starts?

A. 63
B. 75
C. 83
D. 126
E. 188

(C) To visualize this question, think about a circle as just a line segment joined at its two ends. Let's first cut the circle at the starting point and make it in to a straight line. Notice that cars A and B are at opposite ends of the line traveling towards each other.

A [ ______________________ ] B

We start by solving for the circumference of the park:
C = 2πr.

Plugging 20 into the equation, we get:
C = 2 × 3.14 × 20 = 125.6 miles.

To calculate how long it takes the cars to meet, use the variable T as the time, in hours, that it takes for the cars to meet after car A starts.

When the cars meet, car A will have traveled 60T miles (distance = rate × time) and car B will have traveled 40 × (T – (1/3)) miles (since it left 20 minutes later, it will have been traveling 1/3 of an hour less). Furthermore, the distance both cars will travel combined is 125.6 miles. So we have the equation:

Total Distance = Distance A travels + Distance B travels
125.6 = 60T + 40(T – (1/3))
125.6 = 100T – (40/3).

Then we have approximately: 139 = 100T. So, T = 1.39 hours.This is equivalent to 1.39 × 60 = 83 minutes.

The correct answer is choice (C).
-------------

The answer should be 2 × π × 20 = 60 × T + 60 × 1/3 + 40 × T
T= (2 × π – 1) / 5 Then T should be a little bit bigger than one hour.

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 Post subject: Re: math (test 1, question 19): speed/distancePosted: Sat Jun 19, 2010 1:57 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
In your calculations you've denoted by T the time that car B has traveled. Therefore you need to add 20 minutes to get the time that car A has traveled and you'll get the same answer.

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 Post subject: Re: math (test 1, question 19): speed/distancePosted: Mon Feb 21, 2011 6:24 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Why is it assumed that both cars complete the full circumference? Isn't it possible that they meet somewhere along the track?

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 Post subject: Re: math (test 1, question 19): speed/distancePosted: Mon Feb 21, 2011 6:43 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
They do meet somewhere along the track. We do NOT assume that EACH car completes the circumference.

Since they must meet somewhere on the circumference, each car travels from the starting point till the meeting point. Clearly, these distances make up the circumference:

(The path of car A is marked in blue and the path of car B is marked in red).

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The text passage contains a mathematical question and an answer to that question. The question is about calculating the time it takes for two cars traveling in opposite directions around a circular park to meet, given their speeds and the time difference in their departure. The answer is provided, explaining the steps to solve the problem and concluding that the correct answer is 83 minutes, which corresponds to choice (C).
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
It is currently Sun Sep 22, 2019 7:37 pm

 All times are UTC - 5 hours [ DST ]

 Page 1 of 1 [ 4 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: GMAT Speed / Distance / TimePosted: Sat Jun 19, 2010 1:53 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
A similar question is here:

-----------

In the figure above, car A and car B travel around a circular park with a radius of 20 miles. Both cars leave from the same point, the START location shown in the figure. Car A travels counter-clockwise at 60 miles/hour and car B travels clockwise at 40 miles/hour. Car B leaves 20 minutes after car A. Approximately how many minutes does it take for the cars to meet after car A starts?

A. 63
B. 75
C. 83
D. 126
E. 188

(C) To visualize this question, think about a circle as just a line segment joined at its two ends. Let's first cut the circle at the starting point and make it in to a straight line. Notice that cars A and B are at opposite ends of the line traveling towards each other.

A [ ______________________ ] B

We start by solving for the circumference of the park:
C = 2πr.

Plugging 20 into the equation, we get:
C = 2 × 3.14 × 20 = 125.6 miles.

To calculate how long it takes the cars to meet, use the variable T as the time, in hours, that it takes for the cars to meet after car A starts.

When the cars meet, car A will have traveled 60T miles (distance = rate × time) and car B will have traveled 40 × (T – (1/3)) miles (since it left 20 minutes later, it will have been traveling 1/3 of an hour less). Furthermore, the distance both cars will travel combined is 125.6 miles. So we have the equation:

Total Distance = Distance A travels + Distance B travels
125.6 = 60T + 40(T – (1/3))
125.6 = 100T – (40/3).

Then we have approximately: 139 = 100T. So, T = 1.39 hours.This is equivalent to 1.39 × 60 = 83 minutes.

The correct answer is choice (C).
-------------

The answer should be 2 × π × 20 = 60 × T + 60 × 1/3 + 40 × T
T= (2 × π – 1) / 5 Then T should be a little bit bigger than one hour.

Top

 Post subject: Re: math (test 1, question 19): speed/distancePosted: Sat Jun 19, 2010 1:57 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
In your calculations you've denoted by T the time that car B has traveled. Therefore you need to add 20 minutes to get the time that car A has traveled and you'll get the same answer.

Top

 Post subject: Re: math (test 1, question 19): speed/distancePosted: Mon Feb 21, 2011 6:24 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
Why is it assumed that both cars complete the full circumference? Isn't it possible that they meet somewhere along the track?

Top

 Post subject: Re: math (test 1, question 19): speed/distancePosted: Mon Feb 21, 2011 6:43 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
They do meet somewhere along the track. We do NOT assume that EACH car completes the circumference.

Since they must meet somewhere on the circumference, each car travels from the starting point till the meeting point. Clearly, these distances make up the circumference:

(The path of car A is marked in blue and the path of car B is marked in red).

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 4 posts ]

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#### Who is online

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 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions
user
The text passage contains a mathematical question and an answer to that question. The question is about calculating the time it takes for two cars traveling in opposite directions around a circular park to meet, given their speeds and the time difference in their departure. The answer is provided, explaining the steps to solve the problem and concluding that the correct answer is 83 minutes, which corresponds to choice (C).

TYPE: SINGLE_QUESTION_WITH_ANSWER