h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Two ferry boats start moving at the same instant from opposite sides of the h2g2 River, one boat going from the Aroma Café to the Cheshire Grin Inn, and the other from the Cheshire Grin Inn to The Aroma Café. One boat is faster than the other, so they meet at a point 720 yards from the nearest shore. After arriving at their destinations, each boat remains for 10 minutes to change passengers before starting on the return trip. The boats meet again at a point 400 yards from the other shore. What is the exact width of the river?

er.. 1120 yards?

2320, i'm not sure though, my math sucks

Surely this is impossible to work out unless you know how much faster one of the boats is travelling. Or by knowing how long it took one of the boats to cross.
My head hurts!

No, it should be possible all right. It is just very hard.

*glad I can pretend I'm not trying today, rather than admit I don't know how to do this...*

k - h2IQ Champion

1760 yards.

I think.

So much working out I'm not prepared to check it all though!!!!!

Here's the working out:

Width of river = a
speed of boat 1 (fastest) = x
speed of boat 2 = y
length of time until they meet for the first time = n
length of time until they meet for the second time = m

so

x * n = a - 720
y * n = 720
x * m = 2a - 400
y * m = a + 400

n = (a - 720)/x = 720/y
m = (2a - 400)/x = (a + 400)/y

combining gives y = 720x/(a-720) = (a + 400)x/(2a - 400)
divide both sides by x and multiply out gives
(a * a) - 320a - 288000 = 1440a - 288000
add 288000 to each side and divide by a gives a - 320 = 1440

So a = 1760.

Easy!

Where does the 10 minute wait come into it then?

You can ignore the 10 minute wait, because they both wait.

I have worked it out by a different method (finally!) and have also got 1760 yards.

*boggles*

Well done!

I had got as far as width w = 720+400+(some value greater than 320).

Very glad this wasn't yesterday's question!

By the way, my calculation worked out as 720 + 720 + 720 - 400.

The 10 minute wait does matter surely?
"After arriving at their destinations, each boat remains for 10 minutes to change passengers before starting on the return trip."

Therefore, the fast boat has it's 10 minute wait first. In fact it might even have started on its return journey before the slow boat has its 10 min wait.

Good luck! I'm off out anyway.

I challenge the word river. At best, something this size must be a very wide estuary.

I believe the Mississippi River is a mile wide in places.

I think there are two answers to this question.

Isn't it possible that the fastest boat crosses the river, and gets back to the other boat, before the other boat has crossed the river once ?

Or does the term 'meet' imply that the boats are facing each other?

Very good Polidari...1,760 yeards is indeed the correct answer... or me would have accepted a mile... as they the same thing me thinks... ~grin~ the very first point of this new round of h2iq goes to you...

Thanks Greebo.

I would be honoured if you'd accept this from me...

Nice one

The boyfriend explained how to work this out at the weekend, with lots of drawings of triangles and the like. It took him several goes to get it into my brain. Am incredibly impressed...

k

Thanks Kelli.

How are you enjoying being champion? Have people been stopping you in the street yet????

Sooooooo jealous....