How long is the longest piece of the given Rope?

[chwala]

Homework Statement

See attached

Relevant Equations

Grade 9 Math

I do not seem to understand why the ms answer is (C) 45 m unless i am missing something,

In my working i have the longest piece being;

$x+0.5x+0.25x= 95$

$x=\dfrac{380}{7}= 54.28$m

 

[pbuk]

You have answered the question "each piece is half as long as the previous piece". Was that the question?

 

[chwala]

You have answered the question "each piece is half as long as the previous piece". Was that the question?

I wanted to clarify if the correct answer which according to MS, is 45 meters. If my understanding is incorrect, please let me know and guide me accordingly."

According to me the answer ought to be $54$m.

 

[phinds]

Seems to me you went about it the hard way, but yeah, 54.28

I just looked at the problem and immediately multiplied 95 by 4/7

 

[Mark44]

You have answered the question "each piece is half as long as the previous piece". Was that the question?

I wanted to clarify if the correct answer which according to MS, is 45 meters. According to me the answer ought to be 54m.

Yes, the correct answer for the longest piece is 45 m. The actual problem statement is "each piece is half as long again as the previous piece." That word that you missed is crucial.

 

[Mark44]

Seems to me you went about it the hard way, but yeah, 54.28

Nope. And 4/7 has nothing to do with the problem.

 

[phinds]

Nope. And 4/7 has nothing to do with the problem.

Huh? From the problem description, it seems that you have rope segments of 1, 2, and 4, adding up to 7 units so each segments is its number of unites times 95/7 making the longest one 4*95/7. How is that not right?

 

[Mark44]

Huh? From the problem description, it seems that you have rope segments of 1, 2, and 4, adding up to 7 units so each segments is its number of unites times 95/7 making the longest one 4*95/7. How is that not right?

If the first segment is 1 (meter), the next segment is half again as large, not twice as large.

 

[phinds]

If the first segment is 1 (meter), the next segment is half again as large, not twice as large.

Yes, and you're missing the point.

The segments are, as I specifically said, in the ratio of 1, 2 ,4. if you insist on making that 1, 1/2, 1/4, you STILL have exactly the same ratio between the segments (1, 2, 4). I'm just making the math easier. Your way requires a unit of 1/4 for the first segment, my way requires a unit of 4 for the last segment. IT'S IRRELEVANT. We both have 7 units since each of us gets 1, 2, 4. and both of us get 4*7/95ths for the largest piece.

Did you think it was a co-incidence that I got the right answer?

 

[BvU]

Apparently the expression 'half as long again' means that the second piece is 1.5 time as long as the first etc.

I've seen and heard a lot of stuff almost designed to cause confusion in english. This one takes the cake !

$\$

 

[Mark44]

Yes, and you're missing the point.

No, I think you are misunderstanding the problem statement, where it says that each segment is "half as large again" as the previous piece. I.e., 50% larger. It does NOT say that each piece is twice as larger as the previous piece.

The segments are, as I specifically said, in the ratio of 1, 2 ,4. if you insist on making that 1, 1/2, 1/4,

I'm not doing any such thing. If, as you said, the first segment is 1 (unspecified) unit, then the next segment has to be 1.5 of those units, which is half as large again as the first.

 

[Hill]

Apparently the expression 'half as long again' means that the second piece is 1.5 time as long as the first etc.

I've seen and heard a lot of stuff almost designed to cause confusion in english. This one takes the cake !

$\$

Evidently, it's (old?) British English:

(MW dictionary)

 

[Mark44]

Apparently the expression 'half as long again' means that the second piece is 1.5 time as long as the first

Yes, exactly. That word "again" is crucial here, as I said before.

Some examples:
"Half as long" -- 50% as long as the thing being compared against
"As long as" -- same length "
"Twice as long" - 200% of the length "
"Half as long again as" -- 150% of the length "

The last one has the same meaning as "half again as long."

Evidently, it's (old?) British English:

We also say it in American English.

 

[phinds]

half as large again

 

[BvU]

Of course there also is a formula for 'twice as much again' ?

It's not just the imperial units that are totally unsuitable; the language is a disaster too. Let's switch back to Latin !

$\$

 

[Mark44]

Of course there also is a formula for 'twice as much again' ?

I don't know if I've heard that before, but I'd guess it means the same as three times as much.

 

[OmCheeto]

...

We also say it in American English.

I don't remember hearing it in the last 50 years. I wonder if it's on the brink of being considered archaic. hmmm... You don't sit around reading ancient math textbooks do you?

Homework Statement: See attached
Relevant Equations: Grade 9 Math

I do not seem to understand why the ms answer is (C) 45 m unless i am missing something,

What's the copyright date on your textbook?

 

[DaveC426913]

So: x+1.5x+1.5²x=95
y=x*1.5²
Solve for y.

If I saw the correct solution it is only because I stood on the shoulders of the giants that preceded me.

 

[chwala]

...english language problem I see...causing confusion.

 

[phinds]

...english language problem I see...causing confusion.

Well, for me it was strictly a careless reading. The phrase itself is quite clear, I think.

 

[OmCheeto]

I find it interesting that outside of this thread, over the 23 year history of physicsforums, the phrase has only been used about 3 times. And only one of those uses was in a math forum.

2010, by CRGreathouse; "Self-studying probably takes half again as long as learning in a class..."

2007, by madphysics; "...mutations in worms (C. elegans) say that it is possible to live half again as long as normal."

2018, sophiecentaur; "If these wires are close together and more or less parallel then the first sniff of Energy from the battery will arrive after one year (times a factor which will depend on the wires and their insulation - possibly half as long again."

There's another poster that uses 2 variations of the phrase, but it's in the Science Fiction and Fantasy Media forum, and I suspect that it's use was more for artistic merit than anything else.

 

[Mark44]

I find it interesting that outside of this thread, over the 23 year history of physicsforums, the phrase has only been used about 3 times. And only one of those uses was in a math forum.

That's more recent than the 50 years you cited as not having heard the phrase. It may well be somewhat archaic, though.

 

[pbuk]

"Half as [much/long/many etc] again" is still in common colloquial usage in the UK although I suspect it is no longer wording that would be used in an exam question.

I believe "half again as ..." is an Americanism - I have never heard or seen it in the UK.

 

[OmCheeto]

I was going to mention that I doubt many American youths use the phrase, when low and behold...

Challenge 22: Half Again As Big​

Greg Bernhardt​

2014​

​

I'm pretty sure he's at least half again younger than I.

 

[phinds]

I don't know if I've heard that before, but I'd guess it means the same as three times as much.

That's what it sounds like to me but I'll bet it's not what is always intended.