Final answer:
By setting up an equation based on the work rates of Kyle and Jane and their combined work rate, we find that Kyle takes 5 hours to complete the job alone and Jane takes 20 hours.
Step-by-step explanation:
To determine how long it takes Kyle and Jane to do the job alone, we set up an equation based on their individual work rates and their combined work rate. Let Kyle's time to do the job alone be x hours, then Jane's time is x + 15 hours, because Kyle does the job in 15 hours less time than Jane. They can do the job together in 4 hours.
Work rate is often expressed as the reciprocal of time (job per hour). Kyle's work rate is 1/x and Jane's is 1/(x + 15). Together, their rates add up to do 1 job in 4 hours, hence 1/x + 1/(x + 15) = 1/4. Multiplying through by 4x(x + 15) to clear denominators gives: 4(x + 15) + 4x = x(x + 15), which simplifies to 4x + 60 + 4x = x^2 + 15x, and further to x^2 + 7x - 60 = 0.
Factoring the quadratic equation, we get (x + 12)(x - 5) = 0. So, x can be 5 or -12, but time can't be negative, so x = 5. This means that Kyle takes 5 hours to do the job alone, and Jane takes 20 hours.