Worded Prolem (INC).docx

8/14/2019 Worded Prolem (INC).docx

1/8

Two hoses are used to fill a water trough. The first hose can fill it in 20 minutes while the second hose

needs only 16 minutes. If the second hose is used for the first 4 minutes and then the first is also used,

how long will the first hose be used?

What are their rates of filling the trough?

Hose 1: ( 1 trough ) / ( 20 min )Hose 2: ( 1 trough ) / ( 16 min )

How much of the trough does hose 2 get

filled in the 1st 4 minutes?

That means there is of the trough

left to be filled using both hoses

Let = time to fill 3/4 of trough with both hoses

---------

Add their rates of filling to get the rate

with both filling

Multiply both sides by

Multiply both sides by

min

sec

The 1st hose will be used for 6 min and 40 sec

check answer:


2/8

( error is from rounding )

OK

Together John and Michael can paint a wall in 18 minutes. Alone John needs 15 minutes longer to paintthe wall than Michael needs. How much time does John and Michael each need to paint the wall by

himself?

The equation to solve is . The LCD is 18 t( t+ 15).

Michael needs 30 minutes to paint the wall by himself and John needs 30 + 15 = 45 minutes.


3/8

Tiburcio can paint a certain room in 1 day.

His daughter Alma can paint it in 2 days.

After Tiburcio has been working for several hours, his daughter helped him and together they finished

the job in 3 hours.

How many hours did Tiburcio work alone?

Assume an 8-hour working day.

Let t = time that Ti worked alone

Let the completed job = 1 (a painted room)

:

A shared work equation, (time in hrs)

%28%28t%2B3%29%29%2F8 + 3%2F16 = 1

multiply by 16, cancel the denominators, resulting in:

2(t+3) + 3 = 16

2t + 6 + 3 = 16

2t = 16 - 9

2t = 7

t = 7/2

t = 3.5 hrs worked by Ti alone

:

:

See if that checks out on a calc:

6.5%2F8 + 3%2F16 =

.8125 + .1875 = 1


4/8

An experienced worker can unload a truck in one hour forty minutes. When he works

together with a trainee, they can unload the truck in one hour. How long would the trainee

need to unload the truck if he works alone?

-----

exp worker rate = 1/100 job/min

together worker rate = 1/60 job/mintrainee worker rate = 1/x job/min

===============================================

Equation:

rate + rate = together rate

1/100 + 1/x = 1/60

-----

Multiply thru by 100*60x to get:

-----------------------------------

60x + (100*60) = 100x

-------

40x = 6000

x = 150 minutes (time for the trainee to do the job alone)


5/8

The time required for two examinees to solve the same problem differs by two minutes. Together they

can solve 32 problems in one hour. How long will it take for the slower problem solver to solve the

problem?

Let the slower examinee E1 take x min to solve a problem

Then the other one, E2, takes (x-2) min to solve a problem

So in 1 min, E1 can solve 1/x of a problem.

In one hour, E1 solves 60/x problems

Similarly, in one hour, E2 solves 60/(x-2) problems

Together they solve 60%2Fx+%2B+60%2F%28x-2%29+=+60%282%2Ax+-+2%29%2F%28x%2A%28x-

2%29%29+=+32

120%2A%28x-1%29%2F%28x%2A%28x-2%29%29+=+32

Dividing by 8, and cross multiplying

15%2A%28x-1%29+=+4%2Ax%2A%28x-2%29

15%2Ax+-+15+=+4%2Ax%5E2+-+8%2Ax

4%2Ax%5E2+-+23%2Ax+%2B+15+=+0 which is a standard quadratic equation

Solving by factorizing

4%2Ax%5E2+-+20%2Ax+-+3%2Ax+%2B+15+=+0


6/8

4%2Ax%2A%28x+-+5%29+-+3%2A%28x+-+5%29+=+0

%284%2Ax+-+3%29%2A%28x+-++5%29+=+0

x = 3/4 or x = 5

If x = 3/4, it means that the slower examinee takes 3/4 min to solve the problem

and the faster one takes (x - 2) = -1.25 min! This is not possible.

So x = 5 is the time taken by E1, the slower examinee

E2 takes 5 - 2 = 3 min to solve a problem

Check: In one hour, E1 solves 60/5 = 12 problems

E2 solves 60/3 = 20 problems.

Together they solve 12+20 = 32 - correct!


7/8

working together, matt and juan can restock a store's shelves in 2 hours 24 minutes. alone juan needs

two hours longer than matt needs. how long does matt need to restock the shelves when working

alone?

orking together, matt and juan can restock a store's shelves in 2 hours 24 minutes.

alone juan needs two hours longer than matt needs.how long does matt need to restock the shelves when working alone

:

Let x = Matt's time working alone

then

(x+2) = Juan's time alone

:

Let the completed job = 1

:

Change 2 hrs 24 min to hrs: 2 hrs & 24/60 = 2.4 hrs

:

+ = 1

Multiply x(x+2), results:

2.4(x+2) + 2.4x = x(x+2)

:

2.4x + 4.8 + 2.4x = x^2 + 2x

:

4.8x + 4.8 = x^2 + 2x

:

A quadratic equation0 = x^2 + 2x - 4.8x - 4.8

;

x^2 - 2.8x - 4.8 = 0

Factor

(x - 4)(x + 1.2) = 0

Positive solution

x = 4 hrs, Matt alone

;

:

check solution: (Juan's time = 6 hrs)

+ =

.6 + .4 = 1


8/8

Katy left her house on a bicycle heading north at 8 mph. At the same time, her sister Mollyheaded south at 12 mph. How long will it take for them to be 24 miles apart?

The distance between them is increasing at the rate of 8 + 12 = 20 mph. The question then

becomes How long will it take a body moving 20 mph to travel 24 miles?

Let trepresent the number of hours each girl is traveling.

The girls will be 24 miles apart after hours or 1 hour 12 minutes.

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