SOLUTION: At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the
Algebra.Com
Question 1199482: At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people. Calculate the lower bound for the number of minutes it takes for all the people to leave.
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
p = number of people
The true value of p is unknown, but we know that it rounds to 29800 when rounding to the nearest hundred people.
The smallest p could be is 29750 since that rounds to 29800.
The largest is 29849; note that 29850 rounds to 29900.
We have this interval
----------------------------------------------------
r = the rate in which the people leave
This rate is in "people per minute".
Like p, the true value of r is unknown.
The midpoint of 350 and 400 is (350+400)/2 = 375, which represents the smallest value r could be if we round to the nearest 50.
The value 374 would round to 350.
On the other side of the spectrum, (400+450)/2-1 = 425-1 = 424 rounds to 400 as well when rounding to the nearest 50.
The value 425 rounds to 450.
To wrap this section up, you have this interval
----------------------------------------------------
Summary so far:
where p is the number of people and r is the rate in which they leave (in people per minute).
If we have the smallest number of people (29750) and the highest rate in which they leave (424), then we'll get the lower bound of how long it takes everyone to leave.
This can be thought of as the floor value.
time = (number of people)/(rate)
time = (29750)/(424)
time = 70.1650943396227
time = 70.165
----------------------------------------------------
Answer: Approximately 70.165 minutes.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
The lower bound of the number of minutes it takes for all the people to leave is when the attendance is as low as possible and the rate at which they leave is as high as possible.
The lowest possible attendance (29800 plus or minus 50) is 29750.
The highest possible rate of leaving (400 plus or minus 25) is 425.
ANSWER: 29750/425 = 70 minutes
RELATED QUESTIONS
At a football match,there were 250 more men than women.The number of children was twice... (answered by ikleyn)
At a football match,there were 250 more men than women.The number of children was twice... (answered by josmiceli)
The ratio of the number of the men to the number of women at a football match was 4:3.The (answered by josmiceli)
There are 200 people at a football match
120 of them are male
What percentage are... (answered by jorel1380)
The 90 members of a sports club play at
least one of the games tennis, football and... (answered by ikleyn)
Which of these pairs of events are mutually exclusive?
A.winning a football match and... (answered by JulietG)
There are 50,000 people at a stadium watching a soccer match, and 40,000 of them are... (answered by stanbon)
There are 50,000 people at a stadium watching a soccer match, and 40,000 of them are... (answered by poliphob3.14,ewatrrr)
In Faroe island, a sports training camp provides 3 different sections: one in Squash, one (answered by ikleyn)