Jon and his twin sister, together with their 3 younger brothers

Question

Jon and his twin sister, together with their 3 younger brothers, are wrapping presents. Each of the younger brothers can wrap presents at \(\frac{1}{4}\) of the rate that Jon and their older sister can each wrap presents. If all 5 children wrap presents at the same time, in what fraction of the time that it would take Jon and his twin sister to wrap 10 presents together will all 5 children working together take to complete the task?

\(A)\frac{2}{11}\\
B)\frac{4}{11}\\
C)\frac{8}{11}\\
D)\frac{11}{8}\\
E)\frac{11}{2}\)

A)\frac{2}{11}
B)\frac{4}{11}
C)\frac{8}{11}
D)\frac{11}{8}
E)\frac{11}{2}

chetan2u · Answer

Each of the younger brothers can wrap presents at  \frac{1}{4}  of the rate that Jon and their older sister can each wrap presents
Means
both jon and the sister are equal to 4 younger brothers combined in work..

So jon is equal to 4 and sister is equal to 4, thus both combined equal to 4+4=8..
Total working hands in terms of capability of younger brothers = 4+4+3=11
Out of these 11, jon and sister are equivalent of 8 brothers, this they do 8/11 of total work

C

guptakashish02 · Answer

Hi  chetan2u  , 
You have written "both jon and the sister are equal to  4 younger brothers  combined in work.."
But we have 3 younger brothers.

fskilnik · Answer

Let´s say Jon (J) is able to wrap 4 presents per minute, and the same is valid for his twin sister (T).

Hence each younger brother (Y) can wrap 1 present per minute.

? = \frac{{{	ext{Time}}\left( {J \cup T \cup 3Y} ight)}}{{\,{	ext{Time}}\left( {J \cup T} ight)\,}}

During 1 min: J and T can wrap 8 presents, the whole group (J, T and 3Y) can wrap 11 presents.

The ratio (11/8) is the rate of jobs  any interval of time ] of (J, T and 3Y united) to (J and T united).

Our FOCUS, i.e., the rate of time  any given job ] of (J, T and 3Y united) to (J and T united) is its reciprocal:

? = \frac{{{	ext{Time}}\left( {J \cup T \cup 3Y} ight)}}{{\,{	ext{Time}}\left( {J \cup T} ight)\,}} = \frac{8}{{\,11\,}}

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

Jon and his twin sister, together with their 3 younger brothers

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