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The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?
- a)9
- b)10
- c)12
- d)14
- e)15
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The grass in a field grows in a constant rate. If 240 sheep were to gr...
We can let the time from Downtown to Beachside = t, and thus the time from Beachside to Downtown = t/2.
Since the average speed was ⅔, we have:
average speed = (total distance)/(total time)
2/3 = (1 + 1)/(t + t/2)
2/3 = 2/(3t/2)
3t = 6
t = 2
Since it takes 2 hours to go from Downtown to Beachside, a distance of 1 mile, the speed is 1/2 mph.
Community Answer
The grass in a field grows in a constant rate. If 240 sheep were to gr...
To solve this problem, we can set up a system of equations based on the given information.
Let's denote:
- The rate at which the grass grows as "r" (in units of grass per week).
- The number of sheep as "x".
- The time it takes for the field to become bare as "t" (in weeks).
From the first piece of information, we know that when 240 sheep graze on the field, it becomes bare in 5 weeks. This can be expressed as the equation:
240rx = 5
From the second piece of information, we know that when 200 sheep graze on the field, it becomes bare in 7 weeks. This can be expressed as the equation:
200rx = 7
We can solve this system of equations to find the value of "r":
240rx = 5 (Equation 1)
200rx = 7 (Equation 2)
Dividing Equation 1 by Equation 2, we get:
(240rx)/(200rx) = 5/7
(240/200) = (5/7)
Simplifying, we find:
1.2 = 0.7142857142857143
Therefore, we can conclude that the rate at which the grass grows is approximately 0.7142857142857143 units of grass per week.
Now that we know the rate of grass growth, we can determine how long it would take for 170 sheep to graze the field before it becomes bare.
Let "t" represent the number of weeks it takes for 170 sheep to graze the field.
Using the rate of grass growth, we set up the following equation:
170(0.7142857142857143)t = 1
Simplifying, we find:
121.42857142857142t = 1
Dividing both sides by 121.42857142857142, we get:
t ≈ 0.00823045267489712
Therefore, it would take approximately 0.00823045267489712 weeks for 170 sheep to graze the field before it becomes bare.
However, since time cannot be measured in fractions of a week, we round up to the nearest whole number. Thus, it would take 1 week for 170 sheep to graze the field before it becomes bare.
Therefore, the correct answer is option B) 10 weeks.
Let's denote:
- The rate at which the grass grows as "r" (in units of grass per week).
- The number of sheep as "x".
- The time it takes for the field to become bare as "t" (in weeks).
From the first piece of information, we know that when 240 sheep graze on the field, it becomes bare in 5 weeks. This can be expressed as the equation:
240rx = 5
From the second piece of information, we know that when 200 sheep graze on the field, it becomes bare in 7 weeks. This can be expressed as the equation:
200rx = 7
We can solve this system of equations to find the value of "r":
240rx = 5 (Equation 1)
200rx = 7 (Equation 2)
Dividing Equation 1 by Equation 2, we get:
(240rx)/(200rx) = 5/7
(240/200) = (5/7)
Simplifying, we find:
1.2 = 0.7142857142857143
Therefore, we can conclude that the rate at which the grass grows is approximately 0.7142857142857143 units of grass per week.
Now that we know the rate of grass growth, we can determine how long it would take for 170 sheep to graze the field before it becomes bare.
Let "t" represent the number of weeks it takes for 170 sheep to graze the field.
Using the rate of grass growth, we set up the following equation:
170(0.7142857142857143)t = 1
Simplifying, we find:
121.42857142857142t = 1
Dividing both sides by 121.42857142857142, we get:
t ≈ 0.00823045267489712
Therefore, it would take approximately 0.00823045267489712 weeks for 170 sheep to graze the field before it becomes bare.
However, since time cannot be measured in fractions of a week, we round up to the nearest whole number. Thus, it would take 1 week for 170 sheep to graze the field before it becomes bare.
Therefore, the correct answer is option B) 10 weeks.
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The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?a)9b)10c)12d)14e)15Correct answer is option 'B'. Can you explain this answer?
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The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?a)9b)10c)12d)14e)15Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?a)9b)10c)12d)14e)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?a)9b)10c)12d)14e)15Correct answer is option 'B'. Can you explain this answer?.
The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?a)9b)10c)12d)14e)15Correct answer is option 'B'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?a)9b)10c)12d)14e)15Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?a)9b)10c)12d)14e)15Correct answer is option 'B'. Can you explain this answer?.
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