t &w q7

[Saumyojit]

Three diggers dug a ditch of 324 m deep in six days working simultaneously. During one shift, the third digger digs as many metres more than the second as the second digs more than the first. The third digger's work in 10 days is equal to the first digger's work in 14 days. How many metres does the first digger dig per shift?


Work done per day by c ,b ,a = Wc , Wb , Wa

Wc= Wa * 5/7

( Wb + Wa + Wc) * 6 = 324
Wa + Wb + Wc = 54 m per day work combined

ONE shift work
Work of that shift by b= Wb1 , by C = Wc1
Wb1 = (Wa + x) metres ,
Wc1 = ( Wb1 + x ) metres

 

[Dr.Peterson]

Three diggers dug a ditch of 324 m deep

That's a very deep ditch! Are you sure that isn't the length?

Wc= Wa * 5/7

Please explain. This says that C is slower than A. Is C the first or the third digger?

ONE shift work
Work of that shift by b= Wb1 , by C = Wc1
Wb1 = (Wa + x) metres ,
Wc1 = ( Wb1 + x ) metres

Does Wb1 mean Wb times 1 (in which case, why write the 1)? Or is the 1 meant to be a subscript?

I wouldn't introduce yet another variable, x. Just write an equation that says "During one shift, the third digger digs as many metres more than the second as the second digs more than the first", in terms of your three variables.

Then you will have three equations in three unknowns, and can solve by substitution.

 

[Saumyojit]

Are you sure that isn't the length?

sure not length .

Please explain. This says that C is slower than A. Is C the first or the third digger?

third

is the 1 meant to be a subscript?

it is subscript which indicates B's work of that one particular shift specifically.
W subscript b1


Then ,



Wc= Wa * 5/7


Wa + Wb + Wc = 54 m per day work combined

Wb1 = (Wa + x) metres ,
Wc1 = ( Wb1 + x ) metres

I hope that these 4 equations are right and to further solve i need to substitute .

 

[Dr.Peterson]

Wc= Wa * 5/7

No. Did you not think about my question? This says that C is slower than A, and we are told that "The third digger's work in 10 days is equal to the first digger's work in 14 days", which means that C is faster: He digs as much in only 10 days as A does in 14 days. That means you are wrong.

You haven't paid any attention to anything I said. I give up.

it is subscript which indicates B's work of that one particular shift specifically.

Do you realize that they are assuming constant rates, so that whatever is true of one shift is true of every shift? Without that assumption, the problem can't be solved.

sure not length .

If they wrote the problem in a way that made any sense, they would have said "324 m long".

I do find the exact problem in many places; the problem is wrong, if it claims that ditches are dug downward, and can be 324 meters deep. But you don't need to correct that in order to solve the problem; just don't ever apply for a job designing a ditch.

I should add that where I found it, the problem included choices. Have we not warned you to quote the entire problem? Sometimes the choices are an essential part of the problem.

 

[Saumyojit]

ok i got it .

That means you are wrong.

Wc = 7/5 Wa

But how did you know that one shift means it is talking about all the other shifts (other days)

Do you realize that they are assuming constant rates

No i don't realize

 

[Dr.Peterson]

But how did you know that one shift means it is talking about all the other shifts (other days)

(a) Constant rate is a standard assumption in any such problem; we've discussed this before, haven't we? Other typical problems assume everyone works at the same rate (at all times); this one has to be assuming that each person works at their own constant rate.

(b) The problem can't be solved without some such assumption. What would you assume about rates, instead? Why do you think they would tell you about rates during one particular shift, if that doesn't apply to other shifts?

(c) The question it asks is, "How many metres does the first digger dig per shift?" It's asking for one rate, which clearly is assumed to be constant.

The phrase "during one shift" here doesn't mean "during one particular unidentified shift", but "during any one shift", as a way to describe a rate.

 

[Saumyojit]

How many metres does the first digger dig per shift?

this is the biggest hint . "per shift" means generally talking about all the shifts.

the third digger digs as many metres more than the second as the second digs more than the first.

It talks ABOUT work per day .

this little little hints i have to always look for .