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BatMUD Forums > Bs > Re: Pop Quiz: Current Events

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#1
06 Nov 2013 18:29
 
 
A bottle is dropped in a river, known to have a constant 5kph current. A boat
leaves the same point at the same time, travels 75km downstream, then the same
75km upstream, taking 5 hours 45 minutes to make the round trip.

How long, after the bottle is dropped, before the boat passes the bottle while
travelling back upstream?

Shinarae Lluminus

 
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Shinarae
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#2
07 Nov 2013 13:43
 
 
Shinarae wrote:
A bottle is dropped in a river, known to have a constant 5kph current. A boat
leaves the same point at the same time, travels 75km downstream, then the same
75km upstream, taking 5 hours 45 minutes to make the round trip.

How long, after the bottle is dropped, before the boat passes the bottle while
travelling back upstream?

Shinarae Lluminus
I got it as 4 hours 49 minutes and approx 30 seconds
...
My maths is pretty terrible though

 
 
 
Puppaz
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#3
08 Nov 2013 22:18
 
 
Shinarae wrote:
A bottle is dropped in a river, known to have a constant 5kph current. A boat
leaves the same point at the same time, travels 75km downstream, then the same
75km upstream, taking 5 hours 45 minutes to make the round trip.

How long, after the bottle is dropped, before the boat passes the bottle while
travelling back upstream?

Shinarae Lluminus
Don't throw trash into water. Some poor little fish might swim into that
bottle and die because of unexplained reasons.

And I'm suspecting that the boat isn't powered by solar power or some other
non-polluting energy source.

For further information, check www.greenpeace.org.

++C


 
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Calath
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#4
09 Nov 2013 00:52
 
 
Shinarae wrote:
A bottle is dropped in a river, known to have a constant 5kph current. A boat
leaves the same point at the same time, travels 75km downstream, then the same
75km upstream, taking 5 hours 45 minutes to make the round trip.

How long, after the bottle is dropped, before the boat passes the bottle while
travelling back upstream?

Shinarae Lluminus
This is just my bs answer, but I'll go with just over 5h7m.

 
 
 
Xyloid
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#5
10 Nov 2013 09:55
 
 
Shinarae wrote:
A bottle is dropped in a river, known to have a constant 5kph current. A boat
leaves the same point at the same time, travels 75km downstream, then the same
75km upstream, taking 5 hours 45 minutes to make the round trip.

How long, after the bottle is dropped, before the boat passes the bottle while
travelling back upstream?

Shinarae Lluminus
I would say its around 3h. But only if someone was on deck to observe the
bottle!

 
 
 
Nosunrise
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#6
02 Dec 2013 16:46
 
 
Shinarae wrote:
A bottle is dropped in a river, known to have a constant 5kph current. A boat
leaves the same point at the same time, travels 75km downstream, then the same
75km upstream, taking 5 hours 45 minutes to make the round trip.

How long, after the bottle is dropped, before the boat passes the bottle while
travelling back upstream?

Shinarae Lluminus
Vc = 5km/h
d = 75km
T = 5.75h

On the round trip the current will be canceled out for the boat speed

boat base speed = 2d / T
boat upstream speed = (2d / T) - Vc

Downstream trip takes:
d / (2d/T Vc) (~= 2.14h)

Bottle will have traveled

Vc*(d / (2d/T + Vc)) during that time.

Trip remaining to cover is 75 minus what the bottle has covered
(d-(Vc*(d / (2d/T + Vc)))

Which must covered by the boat and bottle combined (let t be the time):
t*((2d / T)-Vc) + tVc = (d-(Vc*(d / (2d/T + Vc)))

Tidy it up a bit

2dt/T - tVc + tVc = d - dVc/(2d/T + Vc)

t = T(d - dVc/(2d/T + Vc)) / 2d

Plus the time for the boat to cover the downstream distance
Ttot = d / (2d/T Vc) + T(d - dVc/(2d/T + Vc)) / 2d

I don't have a calculator.

 
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Malar
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#7
08 Dec 2013 01:54
 
 
Shinarae wrote:
A bottle is dropped in a river, known to have a constant 5kph current. A boat
leaves the same point at the same time, travels 75km downstream, then the same
75km upstream, taking 5 hours 45 minutes to make the round trip.

How long, after the bottle is dropped, before the boat passes the bottle while
travelling back upstream?

Shinarae Lluminus
First you calculate the boat speed s
downstream time + upstream time= total time
75km/(s+5kph)+75km/(s-5kph)=(5+45/60)h
you get s=7.0125kph

Now we know boat speed it's easy to get how long bottle drifted t
at the moment bottle and boat meets:
distance bottle traveled + boat downstream distance + boat upstream distance =
75km + 75km
5kph*t+(7.0125kph+5kph)t+(7.0125kph-5kph)t=75km+75km

t=2 hours 32.48 minutes

 
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Azura
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#9
08 Dec 2013 01:54
 
 
Azura wrote:
Shinarae wrote:
A bottle is dropped in a river, known to have a constant 5kph current. A boat
leaves the same point at the same time, travels 75km downstream, then the same
75km upstream, taking 5 hours 45 minutes to make the round trip.

How long, after the bottle is dropped, before the boat passes the bottle while
travelling back upstream?

Shinarae Lluminus
First you calculate the boat speed s
downstream time + upstream time= total time
75km/(s+5kph)+75km/(s-5kph)=(5+45/60)h
you get s=7.0125kph

Now we know boat speed it's easy to get how long bottle drifted t
at the moment bottle and boat meets:
distance bottle traveled + boat downstream distance + boat upstream distance =
75km + 75km
5kph*t+(7.0125kph+5kph)t+(7.0125kph-5kph)t=75km+75km

t=2 hours 32.48 minutes
this is wrong nvm

 
 
 
Azura
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#10
08 Dec 2013 02:06
 
 
Azura wrote:
Azura wrote:
Shinarae wrote:
A bottle is dropped in a river, known to have a constant 5kph current. A boat
leaves the same point at the same time, travels 75km downstream, then the same
75km upstream, taking 5 hours 45 minutes to make the round trip.

How long, after the bottle is dropped, before the boat passes the bottle while
travelling back upstream?

Shinarae Lluminus
First you calculate the boat speed s
downstream time + upstream time= total time
75km/(s+5kph)+75km/(s-5kph)=(5+45/60)h
you get s=7.0125kph

Now we know boat speed it's easy to get how long bottle drifted t
at the moment bottle and boat meets:
distance bottle traveled + boat downstream distance + boat upstream distance =
75km + 75km
5kph*t+(7.0125kph+5kph)t+(7.0125kph-5kph)t=75km+75km

t=2 hours 32.48 minutes
this is wrong nvm
My final calculationis 5.5 hours, not thinking about this anymore

 
 
 
Azura
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