SOLUTION: 1). A team of workers must to 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? 2). Two pipe

Question 678410: 1). A team of workers must to 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?
2). Two pipes fill a pool in 6 hours together. First pipe fill
5 hours faster than second pipe. In how many hours both
of pipes fill the pool separately.
3). For a field two tractors are working. First tractor
finish the work alone 1 day earlier than second tractor
alone. After they work together for 2 days first tractor
went out and the second tractor finish the rest of field in
0,5 days. In how many days both of the tractors can
finish the field alone?
4). A machine made 208 parts in 3 days. In the first day
the machine made normal amount of parts. In the second
day it made 15% more parts and in the third day it made
10 more parts from the second day. How many parts it
made in every day?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Let p = normal no. of parts per day
Let t = normal no. of days to finish 360 parts
:
Write an equation for each scenario:
= t
When 4 more are done per day:
= t - 1
Replace t
= - 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
:
Find the number of days when 4 more parts a day are completed
360/40 = 9 days, one day earlier
:
:
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.
:
Let x = time required by the 1st pipe
then
(x+5) = time required by the 2nd pipe
Let the complete job = 1
:
A typical shared work equation
+ = 1
multiply by x(x+5), obtain a quadratic equation, and solve it
:
:
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?
:
Let t = time (days) for the 1st tractor alone
then
(t+1) = time for the 2nd tractor alone
Let the completed job = 1
:
+ = 1
do this the same way as no. 2
:
:
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
:
In the second day it made 15% more parts
1.15p = no. on the 2nd day
:
and in the third day it made 10 more parts from the second day.
1.15p + 10
:
How many parts did it make every day?
p + 1.15p + (1.15p+10) = 208
find p
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