Question 1022114
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The previous tutor just pointed you an approach and a way to write the equations.
I will show you how to solve them elementary.
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Rates of more than one eater at the same time are additive.

j, time for Jenny
p, time for Penny
y, time for Lenny
To eat the one gallon on each's own

{{{system(1/j+1/p=1/2,1/p+1/y=1/(1&2/3),1/j+1/p+1/y=1)}}}

Notice that the numerators in all terms are 1, and only a variable is used in every denominator on the left hand members.
An alternative is to not to focus on the times as variables, but to focus on the RATES directly as variables, 
although each rate will still be a fraction.

You might be more comfortable reassigning new variables J = {{{1/j}}}, P = {{{1/p}}} and Y = {{{1/y}}} and forming

J + P     = {{{1/2}}},     (1)    
P +     Y = {{{3/5)}}},     (2)          ( <----- 3/5 = {{{1/(1&2/3)}}} )
J + P + Y = {{{1)}}}.     (3)

Now you have a system of LINEAR equations instead of RATIONAL equations. 

Add equations (1) and (2). You will get

J + 2P + Y = {{{1/2 + 3/5}}} = {{{5/10 + 6/10}}} = {{{11/10}}}.   (4)

Now distract equation (3) from (4). You will get

P = {{{11/10-1}}} = {{{1/10}}}.   (You just have the rate for Lenny!)

Next, from (1) you get J = {{{1/2}}} - P = {{{1/2-1/10}}} = {{{4/10}}} = {{{2/5}}}.

This is Jenny's rate.

Hence, it will take {{{1/J}}} = {{{1/((2/5))}}} = {{{5/2}}} = {{{2}}}{{{1/2}}} hours for Jenny to eat a whole gallon of ice cream by herself.

The problem is solved.
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