John and Jake can cut their parents lawn in an hour and 12 minutes if they work together. Working alone, it takes Jake twice as long as john to finish the job.

Question

How long does it take each working alone?

Answer 1

I am going to write the equation for the solution and then try to explain it.

Let K = Jake's time and H = John's time and K = 2H

(1/H) + (1/K) = 1/(6/5)

(1/H) + (2/H) = 5/6

3/(2H) = 5/6 => 18 = 10H => H = 9/5 and K = 18/5

The reason this equation works is that the reciprocals are rates. If you need further explanation, please send me a message.