Question 1194386

Working together, Jenny and Natalie can assemble a desk in 42/13 hours. Working alone Jenny could have done it in 7 hours. How long would it take Natalie working
alone?
hours.
<pre>Let time Natalie takes, alone, be N
Then Natalie can do {{{1/N}}} of job in 1 hour
Since Jenny takes 7 hours alone, Jenny can do {{{1/7}}} of job in 1 hour
With both completing the job in {{{matrix(1,2, 42/13, hours)}}}, we get the following: {{{matrix(2,3, 1/N + 1/7, "=", 1/(42/13), 1/N + 1/7, "=", 13/42)}}}
                                                                42 + 6N = 13N ------ Multiplying by LCD, 42N
                                                                     42 = 7N
                                       Time Natalie takes, alone, or {{{highlight_green(matrix(1,6, N, "=", 42/7, "=", 6, hours))}}}</pre>