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24 Sep 2009, 12:45
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the distance between station atena and barcena is 90 miles. a train starts from atena to barcens. a bird starts at the same time from barcena straight moving towards the train .on reaching the train, it instaneously turns back and returns to barcena .the bird makes these journeys from barcena to the train and back to barcena till the train reaches barcena .the bird finally returns to rests.calculate the total distance in miles the bird travels in the following 2 cases:
a)the bird flies at 90 miles per hour and the train 60 miles per hour
b)the bird flies at 60 miles per hour and train at 90 miles per hour
a)the bird flies at 90 miles per hour and the train 60 miles per hour
b)the bird flies at 60 miles per hour and train at 90 miles per hour
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25 Sep 2009, 00:27
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A-->B = 90 miles
T from A and B from B
a)Va=90mph; Vb=60mph
Meet in the middle Ta=Tb=T
Distance covered by bird : a=Va.T
Distance covered by train : 90-a=Vb.T
90-a=60*a/90
90-a=2/3*a
a=3/5*90=54 miles
Bird back to Bercene means 54 miles back -->need 54/90 h
Train continue move toward Bercene covered --> 60*54/90=36 miles
Now distance between Train to Bercene (and bird) is 54-36=18 miles
Again as sequence one -->a'=3/5*18=2.7miles
Bird back means 2.7miles -->need 2.7/90 h
Train continue covered --> 60*2.7/90=1.8 miles
a''=3/5*0.9=0.54 miles
bird back --> 0.54/90 h
train continue --> 60*0.54/90=0.36miles
a"'=3/5*0.36=0.072
...as continue in same ways, total miles bird fly is
= 2*3/5*90+2*3/5*3/5*90+...2*(3/5)^n*90 -->(3/5)^n>0
b)Va=60mph; Vb=90mph
a=60*T
90-a=90*T
=90/60*a
a=2/5*90
Bird fly=2*(2/5)*90*(2/5)^(n-1)
Anyone has better and faster solution? HELP!
T from A and B from B
a)Va=90mph; Vb=60mph
Meet in the middle Ta=Tb=T
Distance covered by bird : a=Va.T
Distance covered by train : 90-a=Vb.T
90-a=60*a/90
90-a=2/3*a
a=3/5*90=54 miles
Bird back to Bercene means 54 miles back -->need 54/90 h
Train continue move toward Bercene covered --> 60*54/90=36 miles
Now distance between Train to Bercene (and bird) is 54-36=18 miles
Again as sequence one -->a'=3/5*18=2.7miles
Bird back means 2.7miles -->need 2.7/90 h
Train continue covered --> 60*2.7/90=1.8 miles
a''=3/5*0.9=0.54 miles
bird back --> 0.54/90 h
train continue --> 60*0.54/90=0.36miles
a"'=3/5*0.36=0.072
...as continue in same ways, total miles bird fly is
= 2*3/5*90+2*3/5*3/5*90+...2*(3/5)^n*90 -->(3/5)^n>0
b)Va=60mph; Vb=90mph
a=60*T
90-a=90*T
=90/60*a
a=2/5*90
Bird fly=2*(2/5)*90*(2/5)^(n-1)
Anyone has better and faster solution? HELP!
Archived Topic
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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