If Jesus does a job in 21 hours less time than Cassie and they can do the job together in 10 hours how long will it take each to do the job alone ?

1. Start with the combined work rate equation:

\frac{1}{C} + \frac{1}{C - 21} = \frac{1}{10}

2. Find a common denominator and combine the left-hand side:

\frac{(C - 21) + C}{C(C - 21)} = \frac{1}{10}

3. Simplify the numerator:

\frac{2C - 21}{C(C - 21)} = \frac{1}{10}

4. Cross-multiply to clear the fraction:

10(2C - 21) = C(C - 21)

5. Expand and simplify the equation:

20C - 210 = C^2 - 21C

6. Combine like terms to form a quadratic equation:

C^2 - 41C + 210 = 0

7. Solve the quadratic equation using the quadratic formula:

C = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Where \( a = 1 \), \( b = -41 \), and \( c = 210 \).

8. Plug in the values:

C = \frac{41 \pm \sqrt{41^2 - 4 \cdot 1 \cdot 210}}{2 \cdot 1}

C = \frac{41 \pm \sqrt{1681 - 840}}{2}

C = \frac{41 \pm \sqrt{841}}{2}

C = \frac{41 \pm 29}{2}

9. Calculate the two potential solutions for \( C \):

C = \frac{41 + 29}{2} = 35

and

C = \frac{41 - 29}{2} = 6

10. Since C represents the time (in hours) for Cassie alone, and time can't realistically be 6 hours because Jesus would then take negative time (-15 hours), we discard that solution.

Hence, C = 35 hours for Cassie, and

C - 21 = 14 hours for Jesus.

Therefore, it will take Cassie 35 hours and Jesus 14 hours to complete the job alone.

\boxed{35 \text{ hours for Cassie, 14 \text{ hours for Jesus}}}