t&w q6

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Saumyojit

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According to a plan, a drilling team had to drill to a depth of 270 metres below the ground level. For the first three days the team drilled as per the plan. However, subsequently finding that their resources were getting underutilised according to the plan, it started to drill 8 metres more than the plan every day. Therefore, a day before the planned date they had drilled to a depth of 280 metres. The metres of drilling plan for each day was


(x metres * 3) + (x+ 8) metres * Rest of days = 280

3 + Rest of days = Planned Date -1 (total work is finished before one day of planned date)


What if everything was going according to the plan , x metres per day * Planned days = 270 metres

planned days = 270 / x

Then , (3 + Rest of days) x = 270 -x

=> x= (270 - Rest of Days * x ) / 4

Any hint further?
 
Jomo said:
Yes, here is a hint. Define your variables.
Click to expand...
x = how much meters of digging per day

Rest of days = When the digging is X + 8 meters per day more, then the no of days it is taking to dig .


Planned Date or Days = No of days it actually should take if digging x meters per day
 
Saumyojit said:
(x metres * 3) + (x+ 8) metres * Rest of days = 280
3 + Rest of days = Planned Date -1 (total work is finished before one day of planned date)
What if everything was going according to the plan , x metres per day * Planned days = 270 metres

planned days = 270 / x
Then , (3 + Rest of days) x = 270 -x
=> x= (270 - Rest of Days * x ) / 4
Click to expand...

Let's use some readable variable names, and clean up what you wrote a little:

3x + (x + 8) r = 280​
3 + r = p - 1​
x p = 270​
​
p = 270 / x​
Then , (3 + r) x = 270 - x => x = (270 - rx ) / 4​

You have three variables, x, p, and r, and three equations. You've eliminated p from the last two equations; now eliminate r between the first equation and the final equation you wrote. You can expect to get a quadratic equation in x.

I did it a little differently; in effect, I first used your second equation to express r in terms of p and put that into the first equation, so that I had two equations in your x and p; then I substituted your fourth equation (which came from the third) into the first to eliminate p.
 
3 * (270 - rx) / 4 + ( (270 - rx )/ 4 + 8 ) r = 280

(810 - 3rx ) / 4 + (( 270 - rx + 32 ) * r )/4 = 280

- xr^2 + r * (- 3x + 302) - 310 = 0

...... then?
 
Saumyojit said:
3 * (270 - rx) / 4 + ( (270 - rx )/ 4 + 8 ) r = 280

(810 - 3rx ) / 4 + (( 270 - rx + 32 ) * r )/4 = 280

- xr^2 + r * (- 3x + 302) - 310 = 0

...... then?
Click to expand...
You still have both variables, so you've accomplished nothing. You didn't follow my suggestion, though you thought you did.

I guess I should have explicitly told you that your last line, as written, was useless:
Dr.Peterson said:
x = (270 - rx ) / 4
Click to expand...
It might become useful if you solve it for r. It may look to you as if it is solved for x, but it is not, since x is on both sides. That's why using it didn't eliminate a variable.

Always pay attention to the goal!
 
Dr.Peterson said:
You still have both variables, so you've accomplished nothing. You didn't follow my suggestion, though you thought you did.

I guess I should have explicitly told you that your last line, as written, was useless:

It might become useful if you solve it for r. It may look to you as if it is solved for x, but it is not, since x is on both sides. That's why using it didn't eliminate a variable.

Always pay attention to the goal!
Click to expand...
3x + ( x (270 - 4x ) + 8 ( 270 - 4x) ) / x = 280

(-4)x^2 - 39x + 2160 = 0

-4x^2 - 39x + 2160 = 0

x = 18. 8687 metres

But answer is 30 m

I solved it using solver
www.calculatorsoup.com

Quadratic Formula Calculator

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Saumyojit said:
3x + ( x (270 - 4x ) + 8 ( 270 - 4x) ) / x = 280

(-4)x^2 - 39x + 2160 = 0

-4x^2 - 39x + 2160 = 0

x = 18. 8687 metres

But answer is 30 m
Click to expand...
That tells you to check your work! (You should have done that anyway, even if you weren't given an answer; you know you're capable of making mistakes, right?)

The 39 in your equation is wrong. It may help if you write out more steps.
 
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