Two Ferry Problem
How wide is the river?
As usual, please post answers and solutions in
wide enough for both boats?Quote: WizardFerry A leaves the south shore of a river at the same time as ferry B leaves the north shore. They both travel at 90-degree angles to the shore. The pass each other at a point 720 meters from the north shore. They both continue in the same direction, make a 10-minute stop at their respective opposite shores, and turn around. The two ferries pass each other again 400 meters from the south shore. Each ferry travels at its own rate consistently, except the 10-minute shore breaks.
How wide is the river?
As usual, please post answers and solutions inhave a nice day
Sa * t = x - 720
Sb * t = 720
--> (x - 720) / Sa = 720 / Sb
Sb = Sa * 720 / (x - 720)
Sa * t2 = 2x - 400
Sb * t2 = x + 400
--> (2x - 400) / Sa = (x + 400) / Sb
Sb = Sa (x + 400) / (2x - 400)
==> Sa (x+ 400) / (2x - 400) = Sa * 720 / (x- 720)
(x + 400) / (2x - 400) = 720 / (x - 720)
x = 1760
The river is 1760 meters wide.
Let w = width of the river.
So we have two equations solved by t = d/v:
(1): 720/n = (w-720)/s: s/n = (w-720)/720
(2): (w+400)/n = (2w - 400)/s: s/n = (2w-400)/(w+400)
s and n are the same in both equations and therefore the ratio will be the same:
(w-720)/720 = (2w-400)/(w+400)
solve for w:
(w-720)(w+400) = 720(2w-400)
w^2 - 1760w = 0
w = 1760.
PM me for the valid answer
It's pretty simple:
[ spoiler] Answer here [ /spoiler]
Just omit the space before [_spoiler]
Quote: WizardI concur with the answers of Boymimbo and Canyonero. My method was the same as boymimbo's.
As was mine.
Quote: WizardI concur with the answers of Boymimbo and Canyonero. My method was the same as boymimbo's.
Woot! I'm just embarrassed that it took me an hour to figure out. The 10 minute wait is just a ruse to confuse you.
Next time, I'll buy a bunch of camera gear and show me working away at my computer to show you that I'm doing the work. It'll be scintillating stuff. Or maybe I'll do a few hundred trials to prove my answer. I'm telling you, though, the answer that I came up with is the right one!!!
Quote: boymimboNext time, I'll buy a bunch of camera gear and show me working away at my computer to show you that I'm doing the work.
Please post the video on YouTube. How about an over/under line on number of views in the first year?
Quote: WizardPlease post the video on YouTube. How about an over/under line on number of views in the first year?
Are you serious? ;) I was just parodying another famous thread on this forum. I have no interest in broadcasting myself on YouTube -- my life is far too uninteresting for anyone to pay attention to it -- heck sometimes I don't pay attention to myself.
Quote: boymimboAre you serious? ;) I was just parodying another famous thread on this forum. I have no interest in broadcasting myself on YouTube -- my life is far too uninteresting for anyone to pay attention to it -- heck sometimes I don't pay attention to myself.
Come on, don't sell yourself short. I bet you do the dishes sometimes.
Quote: rainmanWhy do I always click the wizards spoiler tag when I know it always says have a nice day?
