Problema Solution
Mike and Dan are mowing a lawn. If Mike mows the lawn by himself, it takes him 2 more hours than it would take if Dan mows the lawn by himself. If they can mow the lawn in 8 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
y = the hours Dan needs to mow the lawn alone
it takes 2 more hours for Mike to mow the lawn by himself than it would take Dan to mow the lawn by himself
x = y + 2
if they mow together they finish the job in 8 hours and in 1 hour they finish 1/8 of the job:
1/x + 1/y = 1/8
by solving the system of equations
x = y + 2
1/x + 1/y = 1/8
we find 2 solutions:
Solution 1:
x = 0.9933
y = - 1.06226
Solution 2:
x = 17.0623
y = 15.0623
we consider only the positive solution where x>0 and y>0 thus we can say that
Mike needs 17.0623 hours to mow the lawn by himself.