Math question

[Dental2000]

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Q) Jane can type 4/3 as fast as Shirley who types 3/2 as fast as beth. Together they complete a 9810-word report. How many words did Shirley type?

a)3270
b)4360
c) 2180
d) 4350
e) cannot be determined


I need a full explanation to it with details as to how you got to the answer. The solution in my book has a pretty bad explanation

 

[PhansterZ]

Q) Jane can type 4/3 as fast as Shirley who types 3/2 as fast as beth. Together they complete a 9810-word report. How many words did Shirley type?

a)3270
b)4360
c) 2180
d) 4350
e) cannot be determined


I need a full explanation to it with details as to how you got to the answer. The solution in my book has a pretty bad explanation

So in terms of speed:

J/S = 4/3
J = 4S/3

S/B = 3/2
B = 2S/3

We know that the total that they all type is 9810 words, so...

J + S + B = 9810

Subbing in for Shirley,

4S/3 + S + 2S/3 = 9810
3S = 9810
S = 3270

Is that clearer?

 

[tehdude]

...or you can just realize almost immediately that Shirley will do 1/3 of the work.

Beth's contribution = x
Shirley's = 3/2x = 1.5x
Jane's = (4/3)(3/2)x = 2x

Their combined effort in any given amount of time would be 4.5x. Shirley does 1.5x or 1/3 of the total.

9810 * 1/3 = 3270

 

[PhansterZ]

...or you can just realize almost immediately that Shirley will do 1/3 of the work.

Beth's contribution = x
Shirley's = 3/2x = 1.5x
Jane's = (4/3)(3/2)x = 2x

Their combined effort in any given amount of time would be 4.5x. Shirley does 1.5x or 1/3 of the total.

9810 * 1/3 = 3270

This is probably the explanation they gave in the book 😉

 

[Dental2000]

Thanks ma peeps...really good explanation(the first one 😀)