Analytical - Motorboat A leaves shore P as B leaves Q; they move across the lake at a constant speed. They meet f

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Motorboat A leaves shore P as B leaves Q; they move across the lake at a constant speed. They meet first time 600 yards from P. Each returns from the opposite shore without halting, and they meet 200 yards from Q. How long is the lake?

Total Answers and Comments: 10

Last Update: November 02, 2006 Asked by: sharad vasisht

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November 21, 2005 01:42:48

Abhijeet Hivarekar

RE: Motorboat A leaves shore P as B leaves Q; they mov...

Distance between shores is 1000 yards

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November 21, 2005 02:30:22

brummerbull

Member Since: November 2005 Contribution: 1

RE: Motorboat A leaves shore P as B leaves Q; they mov...

Distance is 1600 yards

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November 23, 2005 03:41:20

pravin_vaidya

Member Since: November 2005 Contribution: 7

RE: Motorboat A leaves shore P as B leaves Q; they mov...

900 yards

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November 23, 2005 10:47:19

PRI

RE: Motorboat A leaves shore P as B leaves Q; they mov...

1600 yards

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December 01, 2005 02:13:13

RE: Motorboat A leaves shore P as B leaves Q; they mov...

P 600 AB d-600 Q

P d-200 BA 200 Q

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December 02, 2005 11:04:09

sharad vasisht

RE: Motorboat A leaves shore P as B leaves Q; they mov...

Plz tell the exact answer...whether its 1600 12 00 or 900.also with the approach..thanks

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December 03, 2005 12:31:51

sharad_vasisht

Member Since: November 2005 Contribution: 19

RE: Motorboat A leaves shore P as B leaves Q; they mov...

could u plz tell me the approach how the ans is 1600?

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December 28, 2005 06:45:43

vipin

RE: Motorboat A leaves shore P as B leaves Q; they mov...

Correct answer is 1600 yard as first time they met 600 yard from p so the ratio of their speed at first time ll be 600:y-600(let y is total distance)for second meeting ratio ll be (y+200):2(y-100)equate both ratioes u ll get y 1600 yard

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February 01, 2006 00:56:45

Harry

RE: Motorboat A leaves shore P as B leaves Q; they mov...

((x-600)+200)/600 (600+(x+200))/x-600

Solving this equation we get x 1600.

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November 02, 2006 04:26:44

#10

rakrak_2

Member Since: October 2006 Contribution: 17

RE: Motorboat A leaves shore P as B leaves Q; they mov...

600(A) x-600(B)
p--------------------+----------------------------q

x-200(B) 200(A)
p------------------------------------+------------q

600/(x-600) ((x-600)+200) / 600+(x-200)
simplifying:

600/(x-600) (x-400)/(x+400)

600(x+400) (x-600)(x-400)
600x+240000 x^2 -600x -400x + 240000
x^2 1600x
x 1600
so 1600 is the answer.

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