Question

For a certain amount of work,it takes john 6 hours less than tommy,if they both work together,it takes them 13 hours 20 minutes,how long will it take tommy alone to complete the work

Answer 1

T is tommy's time, so tommy's rate is 1/T
John's rate is 1/(t-6)

Ratecombined=rateTommy+rateJohn

job=rate*time
1=(1/t+ 1/(t+6)) 13 1/3

t(t+6)=(t+6 + t)40/3

t^2+66-80t/3-240/3=0

3t^2-806t-62=0 check that

t=(806+-sqrt(806^2+12*62))/6
solve, ignore the negative solution.

check my calcs, I did them in my head (no paper handy)

Answer 2

1/x + 1/(x+6) = 1/(40/3) = 3/40
times 40x(x+6)
40(x+6) + 40x = 3x(x+6)
3x^2 - 62x - 240 = 0
t = (62 ± √6724)/6
= 24 or -3/1/3 , but x > 0

so x = 24

tom alone can do it in 24 hrs, John alone can do it in 30 hours

check:
at combined time,
time of job = 1/(1/24+1/3))
= 1/(3/40) = 40/3
= 13 1/3 hrs