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Photo: Michael Niestedt / DER SPIEGEL
Mike likes Irish beer and prefers to go to the pub.
Max is into light and can therefore often be found in the Bavarian brewery.
One evening everyone is in their favorite pub - but the two decide to swap locations.
They start at the same time and go to the other pub.
Everyone at their own, but always constant, speed.
There is only one way - and so they both meet somewhere between the two bars.
At the meeting point, they discover that Mike has run 200 meters more than Max.
They stand together there for longer and talk about all sorts of things: the best form of beer glass, whether you shouldn't just stand in a pub and whether Ireland is really greener than Bavaria.
After about 20 minutes, Max and Mike continue on their way.
But because both are still completely lost in thought about their lively discussion, they now only go at half the speed.
Mike then needs eight minutes to get to the brewery.
Max, on the other hand, is on the road for 18 minutes before he arrives at the Irish pub.
How long is the distance between the two bars?
Please scroll down for the solution!
Photo: Michael Niestedt / DER SPIEGEL
solution
The route is
1000 meters
long.
My solution consists of a calculation with four equations and four unknowns.
With the well-known equation
Distance = speed * time
I set up four equations for the stretches the two walked: two up to the meeting point, and two from the meeting point.
Icon: enlarge Photo: Michael Niestedt / DER SPIEGEL
a
is the way from the brewery to the meeting point,
a + 200
is the way from the Irish pub to the meeting point.
Mike walks with speed
v
i
, Max has speed
v
a
.
The walking time of the two from the respective pub to the meeting point is
t
.
Then the following four equations apply:
v
a
* t = a
v
i
* t = a + 200
v
a
* 18/2 = a + 200
v
i
* 8/2 = a
From the above two equations for the
path to the meeting point
, I get by dividing:
v
a
/
v
i
= a / (a + 200)
The two equations below for the
path from the meeting point
result:
v
a
/
v
i
= 4 (a + 200) / 9a
So:
a / (a + 200) = 4 (a + 200) / 9a
I shape this to:
9a2 = 4 (a + 200) 2
5a2 - 1600a - 160,000 = 0
a2 - 320a - 32,000 = 0
This equation has only one positive solution - namely a = 400 meters.
Because the distance from pub to pub 2a is + 200 meters, the distance is 1000 meters.
I discovered this puzzle on the mathematik.ch website.
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