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.
+128474 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
