If Mutt and Jeff need to paint a fence Mutt can do the job alone 8 hours faster than Jeff If together they work for 21 hours and finish only 45 of the job how long would Jeff need to do the job alone?

Answer 1

Let us assume Jeff can do the job in x hours.

Then, Mutt can do the job in x-8 hours

In 1 hour, Jeff can do 1/x of the job.

In 1 hour, Mutt can do 1/(x-8) of the job.

Together , they can do 1/x + 1/(x-8) of the job in 1 hour.

In 21 hours, together they can do 21/x + 21/(x-8) of the job.

21/x +21/(x-8) = 45 %

21/x + 21/(x-8) =0.45

21(x-8)+21x=0.45x(x-8)

42x-168=0.45x^2-3.6x

Rearranging, 0.45x^2-45.6x+168=0

Multiply both sides by 100

45x^2-4560x+16800=0

Use the quadratic equation to solve

This equation is of form ax^2+bx+c=0

a = 45 b = -4560 c = 16800

x=[-b+/-sqrt(b^2-4ac)]/2a]

x=[4560 +/-sqrt(-4560^2-4(45)(16800)]/(2)(45)

discriminant is b^2-4ac =17769600

x=[4560 +√(17769600)] / (2)(45)

x=[4560 -√(17769600)] / (2)(45)

x=[4560+4215.400336860071] / 90

x=[4560-4215.400336860071] / 90

The roots are 97.5044 and 3.8289

3.8 cannot be a solution because Mutt finishes the job, 8 hours faster. Therefore, 97.5 % is the answer.

To finish 45 % of the job, assume it takes Jeff 97.5 hours

To finish the whole job, it would take (97.5)(100)/45 = 216.67 hours