river crossing

[Greg Ward]

Two polluting carbon emitting gas guzzling power boats start at the same time from opposite side of the polluted Marrickville River, that is not ebbing or flowing, being full of garbage.

They travel at constant speed at rights angles to the river banks, but one is faster than the other.
They pass at a point 720 metres from the nearest shore.
Both boats remain at the wharf for 10 minutes while they fill with more polluting petroleum before starting back.
On the return trip, they met 400 metres from the other shore.
Once the reach the shore again, they are stoned to death by green Councillors.

How wide is the river?

Greg

[Handyjack]

Does it matter? Their dead!

[Groggy]

1120m

[Greg Ward]

Try this:
Let x be the river width.
On the first trip the ratios of distances travelled by the 2 boats is x-720:720

On the second trip it is:

[Wongo]

2x - 400 : x + 400

.....

[Greg Ward]

Those ratios are equal.


x-720/720 = 2x-400/x+400

(x-720)(x+400) = 720(2x-400)

x2-720x+400x-288000 = 1440x-288000

x2-320x-1440x = 0

x(x-1760) = 0

So the answer is:


Thanks

Greg

ps x2 is x 'squared', I can't make the machine type the correct symbol

[Groggy]

You already gave the answer, it's 'x'

[andrewr79]

After 15 minutes or so trying to remember how to solve these, I instead remembered that I hate maths so instead went and looked at pretty tools I can't afford. I'm feeling much better about not knowing the answer now!

[Wongo]

1760m

[Wongo]

I was a bit worried about the 10min stop by the boats but as it turned out it didn't matter in the end.

[Wongo]

Let x be the width
Let v1 be the velocity faster boat
Let v2 be the velocity slower boat
Let T be the time taken

The boats first meet:
v1/v2 = (x - 720) / 720

Second meet:

v1 = (2x - 400) / (T - 10)
v2 = (x + 400) / (T - 10)

v1/v2 = (2x - 400) / (x + 400)

Therefore (x - 720) / 720 = (2x - 400) / (x + 400)

x = 1760

[Greg Ward]

When this was first mooted, it was in yards, and as we know who are post 1963...

1760 yards equals..... 1........

Good work Scott ( as usual...).

Greg

[Jonzjob]

1760 yards is a mile. Easy!!