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19 Jun 2016, 03:48
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D
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Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?
a) \(2\leq{x}\leq{10}\)
b) \(4\leq{x}\leq{10}\)
c) \(4\leq{x}\leq{12}\)
d)\(4\leq{x}\leq{16}\)
e) \(6\leq{x}\leq{16}\)
a) \(2\leq{x}\leq{10}\)
b) \(4\leq{x}\leq{10}\)
c) \(4\leq{x}\leq{12}\)
d)\(4\leq{x}\leq{16}\)
e) \(6\leq{x}\leq{16}\)
At most 16 and at least 4
26 Jun 2017, 09:04
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genxer123
bimalr9
Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?
a) \(2\leq{x}\leq{10}\)
b) \(4\leq{x}\leq{10}\)
c) \(4\leq{x}\leq{12}\)
d) \(4\leq{x}\leq{16}\)
e) \(6\leq{x}\leq{16}\)
bimalr9, Bunuel, or anyone, how do we assume that the options for travel are on the same line of travel as home to school? a) \(2\leq{x}\leq{10}\)
b) \(4\leq{x}\leq{10}\)
c) \(4\leq{x}\leq{12}\)
d) \(4\leq{x}\leq{16}\)
e) \(6\leq{x}\leq{16}\)
At most 16 and at least 4
Maybe I'm missing something, but I think this question is confusing because it doesn't indicate that the places he visits are either beyond the school on the same line of travel, or between school and home.
It wasn't self-evident, and I had to run the numbers to make sure my Case III below was not a possibility.
There seems to be a Case III: suppose the school is due east of Bill's house. Suppose football practice is due south (or north) of the school. Suppose the friend's house is due south (or north) of the school and football practice.
Then one of the possibilities for "x miles from home" is then the hypotenuse of a right triangle.
What am I missing?
We are interested in the range of x. The range would be the difference between the greatest value of x and the smallest value of x. Both will occur if all 4 destionations are on a straight line.
The greatest value:
H----------S----FB--F
10 + 4 + 2 = 16.
The smallest value:
H----F--FB----S
10 - 4 - 2 = 4
Range: \(4\leq{x}\leq{16}\)
Answer: D.
Hope it's clear.
19 Jun 2016, 05:07
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bimalr9
Bills' school is 10 miles from his home. He travels 4 miles from school to football practice, and then 2 miles to friend's house. If he is then x miles from home, what is the range of possible values for x?
a) \(2\leq{x}\leq{10}\)
b) \(4\leq{x}\leq{10}\)
c) \(4\leq{x}\leq{12}\)
d)\(4\leq{x}\leq{16}\)
e) \(6\leq{x}\leq{16}\)
a) \(2\leq{x}\leq{10}\)
b) \(4\leq{x}\leq{10}\)
c) \(4\leq{x}\leq{12}\)
d)\(4\leq{x}\leq{16}\)
e) \(6\leq{x}\leq{16}\)
At most 16 and at least 4
1.If his football ground and his friend's house lie on the way to his house.
then the distance can be minimum .
10 -(4+2) = 4
2.If his football ground and his friends house lie in the opposite direction from the way to his house.
this will then give us the maximum distance.
10+(4+2) = 16
therefore , x will lie between 4 and 16
