Question 678410
1). A team of workers must finish 360 parts. They finish 4 more parts in a day so they finish the work 1 day earlier. 
In how many days they finish all 360 parts?
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Let p = normal no. of parts per day
Let t = normal no. of days to finish 360 parts
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Write an equation for each scenario:
{{{360/p}}} = t
When 4 more are done per day:
{{{360/(p+4)}}} = t - 1
Replace t
{{{360/(p+4)}}} = {{{360/p}}} - 1
multiply by p(p+4) to get rid of the denominators
360p = 360(p+4) - p(p+4)
360p = 360p + 1440 - p^2 - 4p
combine like terms and form a quadratic equation on the left
p^2 + 4p - 1440 = 0
You can factor this to
(p+40)(p-36) = 0
the positive solution is all we want here
p = 36 parts a day normally
Find the normal number of days to finish 360 parts
360/36 = 10 days
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Find the number of days when 4 more parts a day are completed
360/40 = 9 days, one day earlier
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2). Two pipes fill a pool in 6 hours together.
 First pipe fill 5 hours faster than second pipe.
 In how many hours do both of pipes fill the pool separately.
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Let x = time required by the 1st pipe
then
(x+5) = time required by the 2nd pipe
Let the complete job = 1
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A typical shared work equation
{{{6/x}}} + {{{6/((x+5))}}} = 1
multiply by x(x+5), obtain a quadratic equation, and solve it
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3). For a field two tractors are working. 
First tractor finishes the work alone 1 day earlier than second tractor alone.
 After they work together for 2 days, the  first tractor went out and the second tractor finished the rest of field in 0,5 days.
 In how many days both of the tractors can finish the field alone?
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Let t = time (days) for the 1st tractor alone
then
(t+1) = time for the 2nd tractor alone
Let the completed job = 1
:
{{{2/t}}} + {{{2.5/((t+1))}}} = 1
do this the same way as no. 2
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4). A machine made 208 parts in 3 days.
 In the first day the machine made a normal amount of parts.
let p = the no. made the 1st day
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 In the second day it made 15% more parts
1.15p = no. on the 2nd day
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 and in the third day it made 10 more parts from the second day.
1.15p + 10
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 How many parts did it make every day?
p + 1.15p + (1.15p+10) = 208
find p