Slow Food Movement
It takes me 45 minutes to make dinner. If my four-year-old daughter "helps" me, it takes 60 minutes. Suppose my wife takes 30 minutes to make dinner by herself. How many minutes will it take her if our daughter "helps" her?
Image Credit: Flickr Anais Watterson .
The answer is 36.
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4 solutions
Well done!
And very interesting that you turned this into "pizzas"... :-)
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Oh gosh, I burst out laughing when I read this problem.
Hahaha I don't know why when I read "dinner" I immediately translated it to "pizza". I've added a little note at the beginning so that I don't have to change "pizza" back to "dinner" 10 times. :)
P.S.. I was surprised when it came our to 36 minutes; my initial thought was that it would be closer to 45 minutes. So much for intuition.
It's interesting how one would expect the answer to be around 3 0 × 3 4 = 4 0 minutes, but it is in fact only 3 6 minutes.
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Yeah, I was surprised; I thought I'd done something wrong at first. If Matt took, say, an hour to make dinner, then with his daughter's help it would take them 1 . 5 hours to make dinner together. And if his wife took, say, 20 minutes on her own, then with her daughter it would take 2 2 . 5 minutes to make dinner. These aren't values I would have guessed, either.
They should just all make dinner together; then it would take 20 minutes. :)
No Offence sir, But don't you think this problem is overrated? @Matt Enlow sir
Say daughter retards the work by x minutes. So to prepare a dinner the equation for the portion of work done per minute would be
4
5
1
−
x
1
=
6
0
1
.
∴
x
=
1
8
0
.
So for wife the equation would be
3
0
1
−
1
8
0
1
=
3
6
1
.
∴
w
i
f
e
+
d
a
u
g
h
t
e
r
t
i
m
e
=
3
6
.
Problem is symmetric to man-work problem .....but here the work done by daughter is negative in proportion.......
(1/45)-(1/y)=1/60......................... (1)
(1/30)-(1/y)=1/x...........................(2)
y is work proportion done by daughter which will be negative as observing the problem....
x is total time proportion taken by both of her wife and daughter...
4 5 1 − 1 8 0 1 = 6 0 1
⟹ 3 0 1 − 1 8 0 1 = 3 6 1
Therefore, 36 minutes.
Note: 15 minutes and 6 minutes make a significant difference. To guess for a right answer became the purpose of answering this question.
Answer: 3 6
v = t d . It is speed but not time that is being slowed.
Finishing one preparation within 45 minutes is slowed by certain speed to become finishing one preparation within 60 minutes. With the same amount of slowed down, finishing one preparation within 30 minutes becomes finishing one preparation within 36 minutes. The amount of slowed down or quantity of slowed down is finishing one preparation within 180 minutes!
Just for fun I will assume that Matt's family is having pizza for dinner.
Matt can make 4 3 1 = 3 4 pizzas per hour. If his daughter can "make" r pizzas per hour, then since together they make pizzas at a rate of 1 per hour we have that
3 4 + r = 1 ⟹ r = − 3 1 pizzas per hour.
(The negative rate just means that she slows whomever she is assisting by a rate of 3 1 pizzas per hour.)
Now since Matt's wife is able to make pizzas at a rate of 2 per hour, with her daughter's "help" they can together make
2 + r = 2 − 3 1 = 3 5 pizzas per hour.
Thus together they will take 3 5 6 0 = 5 3 ∗ 6 0 = 3 6 minutes to make one pizza.