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Saumyojit

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A team of copper miners planned to mine 1800 tons of ore during certain number of days. Due to technical difficulties in the one third of the planned number of days, the team was able to achieve an output of 20 tons less than the planned output . To make up for this, the team overachieved for the rest of the days by 20 tons . The end result was the team completed the task one day ahead of time. How many tons of ore did the team initially plan to mine per day (Tons)?

A) 50
B) 200
C) 150
D) 100
E) 250


I found it to be a time and work question .

Wa = Team work rate original

Wb = Work rate when technical glitch was found .


x = No of days it took for the team to originally complete the work .




Wa * x = 1800 --(i)


x/3 * Wb = ( Wa * x/3 ) - 20 ---(ii) the team was able to achieve an output of 20 tons less than the planned output


y = 1800 - ( tons covered in 1/3 Days by team at a work rate of Wb ) --(iii)


Wa * (x - x/3) = y + 20 --(iv) the team overachieved for the rest of the days by 20 tons



Wa * ( (x - 1) - x/3 ) + ( Wb x ) / 3 = 1800 --(v) The end result was the team completed the task one day ahead of time



(vi)-- Tons covered in x/3 days = Wb * x/3


We see that

Wb x = 5400 - Wa (2x -3)

Wb = ( 5400 - Wa ( 2x -3) ) / x




x/3 * Wb = ( Wa * x/3 ) - 20 ---(ii)

Substituting Wb in (ii)

1800 / ( 3 Wa) * ( 5400 / x - Wa ( 2x -3) / x ) = ( Wa x ) / 3 - 20

600 / Wa * 5400 / x - ( 600/Wa * (Wa * ( 2x -3 ) ) / x ) = Wa x / 3 - 20


Substituting 1800 / Wa in place of x

3240000 / Wa x - ( 600 * 2x - 1800 ) / x = (1800 * x ) / ( x * 3 ) - 20

3240000 / (Wa * 1800/ Wa ) - ( (1200x - 1800) / (1800 / Wa ) = 580

......

324 * 10 ^ (4) - 2160000 + 1800Wa = 580 * 1800

1080000 + 1800Wa = 580 * 1800


Wa = (1080000 - 1044000 ) / 1800 = 20 tons


Where am i wrong?
 
Last edited:
Saumyojit said:
A team of copper miners planned to mine 1800 tons of ore during certain number of days. Due to technical difficulties in the one third of the planned number of days, the team was able to achieve an output of 20 tons less than the planned output . To make up for this, the team overachieved for the rest of the days by 20 tons . The end result was the team completed the task one day ahead of time. How many tons of ore did the team initially plan to mine per day (Tons)?

A) 50
B) 200
C) 150
D) 100
E) 250


I found it to be a time and work question .

Wa = Team work rate original

Wb = Work rate when technical glitch was found .


x = No of days it took for the team to originally complete the work .




Wa * x = 1800 --(i)


x/3 * Wb = ( Wa * x/3 ) - 20 ---(ii) the team was able to achieve an output of 20 tons less than the planned output


y = 1800 - ( tons covered in 1/3 Days by team at a work rate of Wb ) --(iii)


Wa * (x - x/3) = y + 20 --(iv) the team overachieved for the rest of the days by 20 tons



Wa * ( (x - 1) - x/3 ) + ( Wb x ) / 3 = 1800 --(v) The end result was the team completed the task one day ahead of time



(vi)-- Tons covered in x/3 days = Wb * x/3


We see that Wb x = 5400 - Wa (2x -3)

Wb = ( 5400 - Wa ( 2x -3) ) / x

1800 / ( 3 Wa) * ( 5400 / x - Wa ( 2x -3) / x ) = ( Wa x ) / 3 - 20

600 / Wa * 5400 / x - ( 600/Wa * (Wa * ( 2x -3 ) ) / x ) = Wa x / 3 - 20


Substituting 1800 / Wa in place of x

3240000 / Wa x - ( 600 * 2x - 1800 ) / x = (1800 * x ) / ( x * 3 ) - 20

3240000 / (Wa * 1800/ Wa ) - ( (1200x - 1800) / (1800 / Wa ) = 580

......

324 * 10 ^ (4) - 2160000 + 1800Wa = 580 * 1800

1080000 + 1800Wa = 580 * 1800


Wa = (1080000 - 1044000 ) / 1800 = 20 tons


Where am i wrong?
Click to expand...
You defined 3 variable in the beginning. What are the 3 equations? Why in the middle of your solution you introduce a new variable, y? Your solution is very difficult to read. I'd like to see 2 separate sections:
1. Definitions of variables and setup of your system of equations.
2. Solution of the system of equations.
 
Description :

Wa = Team work rate original

Wb = Work rate for x/3 days when technical glitch was found .


x = No of days it took for the team to originally complete the work .

y tons = Amount of ores left



Equations:

Wa * x = 1800 --(i)


Planned output for x/3 days = Wa * x/3

x/3 * Wb = ( Wa * x/3 ) - 20 ---(ii) the team was able to achieve an output of 20 tons less than the planned output



y = 1800 - ( tons covered in 1/3 Days by team at a work rate of Wb ) --(iii)


team Working for rest (x- x/3) days at a work rate of Wa

Wa * (x - x/3) = y + 20 --(iv) the team overachieved for the rest of the days by 20 tons



ahead of time = x - 1 days

Wa * ( (x - 1) - x/3 ) + ( Wb x ) / 3 = 1800 --(v) The end result was the team completed the task one day ahead of time



(vi)-- Tons covered in x/3 days = Wb * x/3


lev888 said:
Solution of the system of equation
Click to expand...

Wa * ( (x - 1) - x/3 ) + ( Wb x ) / 3 = 1800 --(v)

From (v)
Wb x = 5400 - Wa (2x -3)

Wb = ( 5400 - Wa ( 2x -3) ) / x




x/3 * Wb = ( Wa * x/3 ) - 20 ---(ii) this is second equation ok?

Substituting Wb in (ii)

1800 / ( 3 Wa) * ( 5400 / x - Wa ( 2x -3) / x ) = ( Wa x ) / 3 - 20

600 / Wa * 5400 / x - ( 600/Wa * (Wa * ( 2x -3 ) ) / x ) = Wa x / 3 - 20


Substituting 1800 / Wa in place of x

3240000 / Wa x - ( 600 * 2x - 1800 ) / x = (1800 * x ) / ( x * 3 ) - 20

3240000 / (Wa * 1800/ Wa ) - ( (1200x - 1800) / (1800 / Wa ) = 580

......

324 * 10 ^ (4) - 2160000 + 1800Wa = 580 * 1800

1080000 + 1800Wa = 580 * 1800


Wa = (1080000 - 1044000 ) / 1800 = 20 tons
 
Saumyojit said:
Description :

Wa = Team work rate original

Wb = Work rate for x/3 days when technical glitch was found .


x = No of days it took for the team to originally complete the work .

y tons = Amount of ores left



Equations:

Wa * x = 1800 --(i)


Planned output for x/3 days = Wa * x/3

x/3 * Wb = ( Wa * x/3 ) - 20 ---(ii) the team was able to achieve an output of 20 tons less than the planned output



y = 1800 - ( tons covered in 1/3 Days by team at a work rate of Wb ) --(iii)


team Working for rest (x- x/3) days at a work rate of Wa

Wa * (x - x/3) = y + 20 --(iv) the team overachieved for the rest of the days by 20 tons



ahead of time = x - 1 days

Wa * ( (x - 1) - x/3 ) + ( Wb x ) / 3 = 1800 --(v) The end result was the team completed the task one day ahead of time



(vi)-- Tons covered in x/3 days = Wb * x/3




Wa * ( (x - 1) - x/3 ) + ( Wb x ) / 3 = 1800 --(v)

From (v)
Wb x = 5400 - Wa (2x -3)

Wb = ( 5400 - Wa ( 2x -3) ) / x




x/3 * Wb = ( Wa * x/3 ) - 20 ---(ii) this is second equation ok?

Substituting Wb in (ii)

1800 / ( 3 Wa) * ( 5400 / x - Wa ( 2x -3) / x ) = ( Wa x ) / 3 - 20

600 / Wa * 5400 / x - ( 600/Wa * (Wa * ( 2x -3 ) ) / x ) = Wa x / 3 - 20


Substituting 1800 / Wa in place of x

3240000 / Wa x - ( 600 * 2x - 1800 ) / x = (1800 * x ) / ( x * 3 ) - 20

3240000 / (Wa * 1800/ Wa ) - ( (1200x - 1800) / (1800 / Wa ) = 580

......

324 * 10 ^ (4) - 2160000 + 1800Wa = 580 * 1800

1080000 + 1800Wa = 580 * 1800


Wa = (1080000 - 1044000 ) / 1800 = 20 tons
Click to expand...
1. Output is output per day. The problem should've made it clear, but the way you interpret it, it doesn't make sense. First period you can sort of make it work, but the second - you can't. What does it mean "the team overachieved for the rest of the days by 20 tons"? The rest of the days? How many? 2/3 of x? But that means that they completed the job in x days, not x-1 days. In any case, I solved it using my interpretation and got 100 tons. Is this correct?
2. You are using multi-letter variables again. Please don't.
3. You have too many variables and your equations are too complicated. I was able to express everything using just the variables for the planned number of days. There are many ways to do it, of course, but your solution seems far from optimal.
4. (iii) does not look like an equation. Feel free to use words when setting things up, but the final system should include variables and operations only.
 
lev888 said:
1. Output is output per day. The problem should've made it clear, but the way you interpret it, it doesn't make sense. First period you can sort of make it work, but the second - you can't. What does it mean "the team overachieved for the rest of the days by 20 tons"? The rest of the days? How many? 2/3 of x? But that means that they completed the job in x days, not x-1 days. In any case, I solved it using my interpretation and got 100 tons. Is this correct?
2. You are using multi-letter variables again. Please don't.
3. You have too many variables and your equations are too complicated. I was able to express everything using just the variables for the planned number of days. There are many ways to do it, of course, but your solution seems far from optimal.
4. (iii) does not look like an equation. Feel free to use words when setting things up, but the final system should include variables and operations only.
Click to expand...
sum is done .
 
Saumyojit said:
no no the answer came i am saying
Click to expand...
The answer came? What?
We spend a significant amount of time solving the problems and writing replies to you. Do you think "sum is done" or "the answer came" is a sufficient acknowledgment of the helpers' efforts?
 
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