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Roger and Bill 04 Oct 2009, 14:57
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Roger and Bill ran home after school. Roger runs at a rate of 6 mph and Bill runs at a rate of 4 mph. When they leave the school at the same time, Roger arrives home .5 hour before Bill.

How long does it take Bill to reach home?

How far do Roger and Bill live from school?



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Roger and Bill 04 Oct 2009, 16:27
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ggarr
Roger and Bill ran home after school. Roger runs at a rate of 6 mph and Bill runs at a rate of 4 mph. When they leave the school at the same time, Roger arrives home .5 hour before Bill.

How long does it take Bill to reach home?

How far do Roger and Bill live from school?
Show more


Roger Bill
Speed 6 mph 4mph
Time t t+.25 h
Distance d d 2d

we have equations,

t (Bill) – t(Roger) = .25

d/4 – d/6 = .25

d = 3

t = 6/d = 6/3 = 2

t+.25 = 2+.25 = 2.25
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Roger and Bill 07 Oct 2009, 02:54
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rlevochkin
ggarr
Roger and Bill ran home after school. Roger runs at a rate of 6 mph and Bill runs at a rate of 4 mph. When they leave the school at the same time, Roger arrives home .5 hour before Bill.

How long does it take Bill to reach home?

How far do Roger and Bill live from school?


Roger Bill
Speed 6 mph 4mph
Time t t+.25 h
Distance d d 2d

we have equations,

t (Bill) – t(Roger) = .25

d/4 – d/6 = .25

d = 3

t = 6/d = 6/3 = 2

t+.25 = 2+.25 = 2.25
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Why have u taken the difference of the time taken as .25? Should it not be .5?
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Roger and Bill 07 Oct 2009, 11:54
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ggarr
Roger and Bill ran home after school. Roger runs at a rate of 6 mph and Bill runs at a rate of 4 mph. When they leave the school at the same time, Roger arrives home .5 hour before Bill.

How long does it take Bill to reach home?

How far do Roger and Bill live from school?
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ANSWER:

You can solve this logically. For every hour that Roger runs, Bill gets 2 miles behind. Bill arrives .5 hours behind Roger so he must be 2 miles back. Thus, at what time is roger 2 miles in front of Bill? A: 1 hour. R=6miles & B=4 miles. So, at the one hour mark, Bill needs to run for an additional .5 hours in order to catch Roger.

Bill takes 1.5 hours to reach home.
Roger and Bill live 6 miles from school.
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Roger and Bill 07 Oct 2009, 12:20
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Algebraically, really straightforward:

6x = 4(x+0.5)

where x is Roger's time



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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