Algebra help? i need a step by step process...?

Question

Bob can plant a flower garden two hours faster than Mary.Working together they can plant the flower garden in 3.5 hours.How long will it take Bob and Mary to plant separately?

Answer 1

Time taken by Bob for whole job = b hrs

Same for Mary = m hrs.

Rate of working of Bob is '1/b' and that of Mary is '1/m'.

Bob can finish the job 2 hrs faster than Mary

b + 2= m

If both of them work together {substituting the above}

1/b + 1/(b+2) = 1/3.5=2/7

2(b +1) = (2/7)[b^2 +2b]

7(b+ 1) =b^2 + 2b

b^2 -5b -7 = 0

b = (5/2) (+/-) sqrt[(5/2)^2 + 7]

= (5/2) (+/-) sqrt[13.25]

= 2.5 (+/-) 3.64

= 6.14 0055 hrs

m = 8.14 0055 hrs