Question 1183788: Johnny drops his kids off at his parents’ house (which is 6 miles from his house), goes to work, goes back to pick up his kids, and heads home. All of these locations are on the same straight road. If Johnny wants to keep his daily driving within 35 miles, how far from his parents’ house can his place of work be? Write an absolute value inequality and solve.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
Johnny drops his kids off at his parents’ house (which is 6 miles from his house), goes to work,
goes back to pick up his kids, and heads home. All of these locations are on the same straight road.
If Johnny wants to keep his daily driving within 35 miles, how far from his parents’ house
can his place of work be? Write an absolute value inequality and solve.
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I read your post and can not understand, how these Johnny's activities are connected with (or related to) driving.
He drops . . . , then he goes . . . , then he goes back . . . , then heads home . . . .
Where and when, considering these activities, he drives ?
And why your post does not describes it in all details ?
Do you want to hide something from the tutors ?
Is it a Math problem, at all ?
As it is worded, your post is only good to confuse a reader, but is infinitely far from to be a TRUE Math problem.
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In this problem, at least three different dispositions are possible :
(a) The parents' home is between the other two locations;
(b) The office is between the other two locations;
(c) The Johnny's home is between the other two locations.
Each configuration creates its own equation, and different configurations/equations produce different answers.
The problem is silent about it, leaving all these cases to the reader to guess or to exercise his (or her) phantasy.
THEREFORE, I firmly believe that the given problem is not a Math problem.
It is a GARBAGE, instead, which should be DELETED in order for do not litter the Internet.
Answer by greenestamps(13215)  (Show Source):
You can put this solution on YOUR website!
Informally, since the locations are in the same straight line, and the distances in both directions are the same, he wants to keep his distance from work less than 35/2=17.5 miles.
Then, since his parents' house is 6 miles from his house, the distance from is parents' house to work has to be less than 17.5-6=11.5 miles
Formally, as the problem requests....
x = distance from his parents' house to work
6+x+x+6 <=35
2x+12 <= 35
2x <= 23
x <= 11.5
ANSWER: His parents' house must be within 11.5 miles of his work.
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