Word for complicated problem

conundrum

is one more powerful synonym of puzzle, problem, enigma, &c. Turns out it has a more interesting etymology than I expected. It’s not from Latin but first shows up as Oxbridge slang

1596 Tom Nashe’s Haue with You to Saffron-Walden; or, Gabriell Harueys Hunt is Vp

So will I… driue [Gabriel Harvey] to confesse himselfe a Conundrum, who now thinks he hath learning inough to proue the saluation of Lucifer.

so apparently it was dog latin for a pedant or ninny at first but then used for puns (first attested in the sermons of a would-be wit:)

16 Dec. 1645, Kingdom’s Weekly Post, p. 76:

This is the man who would have his device alwayes in his sermons, which in Oxford they then called conundrums. For an instance… Now all House is turned into an Alehouse, and a pair of dice is made a Paradice, was it thus in the days of Noah? Ah no!

then an acrostic-like game based on punning answers before finally becoming the headstratcher it is now.

This Lesson (Solving more complicated word problems on joint work) was created by by ikleyn(48006)  : View Source, Show
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Solving more complicated word problems on joint work

This lesson is a continuation of the lesson  Using fractions to solve word problems on joint work  in this site.

While that lesson provides the traditional introductory joint work problems,  this lesson teaches you how to solve a bit more complicated joint work problems.

Problem 1

Working together,  John and Mark can clean a fish tank in  30  minutes.  If Mark works alone,  he can clean it in  50  minutes.
How long does it take John to clean the fish tank working alone?

Solution

Let  j  be the number of minutes for John to clean the tank working alone.

Let  m  be the number of minutes for Mark to clean the tank working alone.

Then John will clean    part of the tank volume per minute.

Correspondingly,  Mark will clean    part of the tank volume per minute.

Working together,  John and Mark will clean    part of the tank volume per minute.  It means that

+ = .       (1)

From the other part of the condition,  Mark is cleaning    part of the tank volume per minute working alone.  It means that

= .             (2)

Substitute  (2)  into  (1).  You will get

+ = .

Hence,

= — = = = = .

Thus  j = = 75 minutes.

Answer.  It will take  75  minutes for Mark to clean the tank working alone.

Problem 2

Pipe  A  can fill a tank in  6  hours.  When both pipe  A  and pipe  B  are used simultaneously,  the tank is filled in 4 hours.
How long,  in hours,  would it take for pipe  B  alone to fill the tank?

Solution

Let  x  be the time,  in hours,  for pipe  B  to fill the tank working alone.

The pipe  A  fills    of the tank volume per hour working alone.

The pipe  B  fills    of the tank volume per hour.

The two pipes,  A  and  B,  working together,  fill   +   of the tank volume per hour.

We are given that this quantity,   + ,  is equal to   of the tank volume.  It gives an equation

+ = .

To solve it,  multiply both sides by  12x.  You will get

2x + 12 = 3x,     or

x = 12.

Answer.  It will take  12  hours for pipe  B  to fill the tank working alone.

Problem 3

An inlet pipe on a swimming pool fills the pool in  12  hours.  The drain pipe empties the pool in  16  hours.

If the pool is    filled and then the inlet pipe and drain pipe are opened,  how long from that time will it take to fill the pool?

Solution

The rate of the inlet pipe is    of the pool volume per hour.

The rate of the drain pipe is    of the pool volume per hour.

The net rate for two pipes working simultaneously is   — =  of the pool volume per hour.

The equation to determine an unknown time  t  for filling    of the remaining volume of the pool is

. = .

It gives  t = 16  hours.

Answer.  16 hours.

Problem 4

Alan can do a job in  12  hours.  Bob can do it in  20  hours.  Carl can do the same job in  30  hours.

How long will it take for Alan,  Bob and Carl to do the job working together?

Solution

Alan’s rate of work is    of the entire job per hour.

That of Bob is    of the entire job per hour.

Carl’s rate of work is    of the entire job per hour.

When the three worker work together,  their net rate of work is

+ + = + + = = =

of the entire work per hour.

It means that the three workers will complete the job in  6  hours,  if they work together.

Answer.  6  hours.

Problem 5

Mario and Julio are working together to wash cars. When they work together they can wash 7 cars in 2 hours.
If Mario works alone he can wash 5 cars in 3 hours. If Julio works alone, how long will it take him to wash 12 cars?

Solution

Let  m  be Mario’s rate when he works alone,  and let  j  be Julio’s rate when he works alone.

From the condition,

m = ,

m + j = .

Hence,  j = (m+j) — m = = =

Therefore,  if Julio works alone,  it will take for him   : = = =  of an hour to wash 12 cars.

Problem 6

A tank has three pipes connected.  The first,  by itself,  could fill the tank in hr,
the second in  2 hr,  and the third in 1 hr and 40 min.  In how many minutes will the tank be filled?

Solution

1.    h = 150 minutes.

    2 hours = 120 minutes.

    1 hour 40 minutes = 100 minutes.


2.  1-st pipe fills  of the tank volume per minute.

    2-nd pipe fills  of the tank volume per minute.

    3-rd pipe fills  of the tank volume per minute.


3.  The three pipes fill   =  =  =  of the tank volume per minute.


4.  Hence, it will take 60 minutes = 1 hour for the three pipes to fill the tank.

My other lessons on joint work problems in this site are

    — Rate of work problems

    — Using Fractions to solve word problems on joint work

    — Using quadratic equations to solve word problems on joint work

    — Solving rate of work problem by reducing to a system of linear equations

    — Solving joint work problems by reasoning

    — Selected joint-work word problems from the archive

    — Joint-work problems for 3 participants

    — HOW TO algebreze and solve these joint work problems ?

    — Had there were more workers, the job would be completed sooner

    — One unusual joint work problem

    — Very unexpected problem on rate of work — HOW TO setup and HOW TO solve

    — Special joint work problems that admit and require an alternative solution method

    — Entertainment problems on joint work

    — Joint work word problems for the day of April, 1

    — OVERVIEW of lessons on rate-of-work problems

Use this file/link  ALGEBRA-I — YOUR ONLINE TEXTBOOK  to navigate over all topics and lessons of the online textbook  ALGEBRA-I.

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