Photo:
THE MIRROR
Every Monday the village cistern is empty and the residents have to fill it with water from the river so that the animals have enough to drink.
Agnes, Bernd and Charles are next Monday.
They meet on Sunday to plan the strenuous action.
They want to start at eight o'clock but don't know exactly how much time it will take them.
Bernd says: »The last time I filled the cistern together with Agnes, it took us four hours.«
"Yeah, right," Agnes says.
“When I filled the cistern with Charles two months ago, we were busy for five hours.” Charles replies: “You know that at over 70 I'm not the fastest either.
When I filled the water reservoir with Bernd alone, he carried exactly twice as many buckets as I did.«
On Monday morning, Charles is at the cistern at eight, as agreed, but there is no sign of Agnes and Bernd.
They've both gone into town for urgent appointments.
Charles has to do the work himself.
When does he finish work?
Charles needs
20 hours
.
Without a break, he would have to work from 8 a.m.
to 4 a.m.
the next day.
A, B and C are the amounts of water that Agnes, Bernd and Charles pump from the river into the cistern each hour.
Then:
(A+B)*4 = (A+C)*5
In addition, the following applies: B = 2C, because Bernd manages twice as much water as Charles.
Plugging this into the equation above gives:
(A+2C)*4 = (A+C)*5
3C = A
(A + C)*5 corresponds to a filling of the cistern.
If we insert A = 3C in it, we get an expression that only contains C as an unknown:
(3C + C)*5 = C*20
This means: Charles alone needs 20 hours to fill the cistern.
Many thanks to the reader Werner Schulz-Simonsen who suggested this task.
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