Problema Solution
Mike and Dan are mowing a lawn. If Mike mows the lawn by himself, it takes him 1 more hours than it would take if Dan mows the lawn by himself. If they can mow the lawn in 7 hours by working together, how long does it take Mike to mow the lawn?
Answer provided by our tutors
let
x = the hours Mike needs to mow the lawn alone, x > 0
y = the hours Dan needs to mow the lawn alone, y > 0
Mike needs 1 hour more to mow the lawn by himself than Dan needs to do the same
x = y + 1
if they mow together they finish the job in 7 hours thus in 1 hour they finish 1/7 of the job:
1/x + 1/y = 1/7
by solving the system of equations
x = y + 1
1/x + 1/y = 1/7
we find consider only the real positive solutions (x > 0, y >0)
x = 14.5178 hours
y = 13.5178 hours
Mike needs 14.5178 hours to mow the lawn by himself.