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Find the distance

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Find the distance

by shashank.ism » Sat Feb 06, 2010 4:40 am
Two boats start from the opposite banks of a river simultaneously. They meet at a distance of 410 m from one of the banks and continue sailing further till they reach the opposite banks. They take rest for 1 hr each and start off the return journey. Now they meet at a distance of 230 m from the other bank. Find the distance between the two banks. Note: (Assume that river water is almost still).

a.)750 m
b.) 840 m
c.) 1100 m
d.) 1200 m
e.)1000 m
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by ajith » Sat Feb 06, 2010 5:22 am
shashank.ism wrote:Two boats start from the opposite banks of a river simultaneously. They meet at a distance of 410 m from one of the banks and continue sailing further till they reach the opposite banks. They take rest for 1 hr each and start off the return journey. Now they meet at a distance of 230 m from the other bank. Find the distance between the two banks. Note: (Assume that river water is almost still).

a.)750 m
b.) 840 m
c.) 1100 m
d.) 1200 m
e.)1000 m
Let the distance between the banks be x meters
speed of first boat be a and the second boat be b

now, 410/a = x-410/b

b/a = (x-410)/410

Now first boat will reach the other bank in x/a time and second boat will reach there in x/b time and they both take rest for 1 hour

when they meet the second time distance travelled by first boat = x+230
distance travelled by second boat = 2x -230

x+230/a = 2x-230/b

b/a = 2x-230/x+230

x-410/410 = 2x-230/x+230

Now, I would substitute the answers and my luck 1000 comes out to work perfectly
{well purists (I have been seeing many of them lately)can solve the quadratic equation and find out}
Last edited by ajith on Sat Feb 06, 2010 5:52 am, edited 1 time in total.
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by shashank.ism » Sat Feb 06, 2010 5:33 am
Let the distance between the banks be x meters
speed of first boat be a and the second boat be b

now, 410/a = x-410/b

b/a = (x-410)/410

Now first boat will reach the other bank in x/a time and second boat will reach there in x/b time and they both take rest for 1 hour

when they meet the second time distance travelled by first boat = x+230
distance travelled by second boat = 2x -230

x+230/a = 2x-230/b

b/a = 2x-230/x+230

x-410/410 = 2x-230/x+230

Now, I would substitute the answers and my luck 1000 comes out to work perfectly
{well for purists (I have been seeing many of them lately)can solve the quadratic equation and find out}
good work ajith..btw when you get this type of quadratic equation with some big numbers...plug in is the best way to solve it..and so you also get the ans same way luckily in 1st attempt..
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