Question

Working together, two people can cut out a large lawn in 2 hr. One person can do the job alone in 1 hr less than the other? How long (to the nearest tenth) would it take the faster worker to do the job? (Let x representthe time of the faster worker).

Answer 1

worker 1 does job in x hours
worker 2 does it in x+1 hours

worker 1 is x hr/job or (1/x) jobs/hr

worker 2 is x+1 hr/job or 1/(x+1) jobs/hr

time for both together is two hr
so
[(1/x)jobs/hr + 1/(x+1) ]2hr = 1job

1/x + 1/(x+1) = .5

(x+1) + x = .5 x(x+1)

2x + 1 = .5 x^2 + .5 x

.5 x^2 - 1.5 x - 1 = 0

x^2 - 3x - 2 = 0

x = [ 3 +/-sqrt (9+8) ]/2

x = 3.56 hr answer
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check
x = 3.56 hr/job
x+1 = 4.56 hr/job

1/3.56 + 1/4.56 = .281 + .219 = .500
sure enough, together the do half the job in an hour