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
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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):
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.
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
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.
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