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# algebra

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Brandon typically takes 2 less hours than Maria to assemble a bicycle if each works alone. Brandon and Maria worked together to assemble a bicycle for 3 hours, and then Maria finished the job without Brandon after an additional 1 hour. How long would it have taken Maria to assemble the bicycle alone? Do not include the units in your answer.

Jun 30, 2022

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Call the part of the bike that Brandon  can assemble in one hr =  1/  x

Call the part that Maria can  assemble in one hour   =  1 / ( x + 2)

Working together  they assemble   1 /x + 1/(x +2)    part of the bike

So

Part of the bike they can  assemble in 3 hours + part Maria can assemble in one  hour =  1

3 [1/x + 1 / (x + 2)]  + (1)( 1/(x+ 2))  = 1

3/x +   ( 4) / (x + 2)  = 1

[ 3( x + 2) + 4x ] / [ x * (x + 2) ] =  1

7x + 6 =  x^2 + 2x

x^2 - 5x - 6 =  0

( x - 6) (x + 1)  =  0

Take the first factor and  set =  0

x = 6

It takes Maria       x + 2 =    8 hours to  assemble the  bike  by herself   Jun 30, 2022