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If Jesus completes 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 complete the job alone

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Answer to a math question If Jesus completes 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 complete the job alone

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Hester
4.8
116 Answers
\text{Given:}

t_J = t_C - 21

\frac{1}{t_J} + \frac{1}{t_C} = \frac{1}{10}

1. Substituting into combined work formula:

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

2. Multiplying by \( t_C(t_C - 21) \):

t_C + (t_C - 21) = \frac{t_C^2 - 21t_C}{10}

3. Combining and simplifying:

2t_C - 21 = \frac{t_C^2 - 21t_C}{10}

20t_C - 210 = t_C^2 - 21t_C

4. Solving quadratic equation:

t_C^2 - 41t_C + 210 = 0

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

5. Finding \( t_C \):

t_C = 35 \, \text{(valid solution)} \qquad t_C = 6 \, \text{(invalid)}

\text{Therefore, the time it takes each to complete the job alone is:}

t_C = 35 \, \text{hours}

t_J = 14 \, \text{hours}

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