MathMaster logo

MathMaster

  1. Home
  2. general
  3. 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 t
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

191

likes
957 views

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

Expert avatar
Hester
4.8
117 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}

Frequently asked questions (FAQs)
What is the integral of the function f(x) = 3x^2 + 2x + 5 with respect to x, using the power rule?
+
Math Question: In a group of 10 people, how many different ways can you choose a committee of 3 members?
+
What is the equivalent of 3.2 x 10^4 in standard notation?
+
New questions in Mathematics
Find two natural numbers whose sum is 230 and their difference is 10. Set up the system and solve it.
2+2
90 divided by 40
Two events E and F are​ ________ if the occurrence of event E in a probability experiment does not affect the probability of event F.
The mean life of a television set is 119 months with a standard deviation of 13 months. If a sample of 67 televisions is randomly selected, what is the probability that the sample mean would be less than 121 months? Round your answer to four decimal places
Convert 78 percent to a decimal
form a key for your lock containing the numbers 2 2 5 8 How many different keys can you form?
Raúl, Gilberto and Arturo are playing golf; The probabilities of winning for each one are as follows: (Raúl wins) = 20% (Gilberto wins) = 0.05% (Arturo wins) = ¾%. Perform operations and order events from least to most probable.
TEST 123123+1236ttttt
cube root of 56
Write the equation of the line that is parallel to y= 4x-7 and has a y- intercept at (0,5)
find missing measure for triangle area = 48 m square base = 10m heaighy = ? m
Two particles of electrical charges Q1=3.8×10-⁶C and q,=4.4×10-⁶C are separated in vacuum by a distance of 4.0.10-⁸ m. Since K=9.0.10⁹ N.m²/C², the intensity of the interaction force between them, in newtons, is?
Below are three 95% CIs (where 𝜎 was known and 𝑥̅happened to be the same); one with sample size 30, one with samplesize 40, and one with sample size 50. Which is which?(66.2, 76.2)(61.2, 81.2)(56.2, 86.2)
Evaluate ab+dc if a=56 , b=−34 , c=0.4 , and d=12 . Write in simplest form.
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
2.3 X 0.8
6(k-7) -2=5
Sarah is lining a square tray with 1 inch square tiles. the side length of the tray is 9 inches. How many tiles does Sarah need?
Matilde knows that, when driving her car from her office to her apartment, she spends a normal time of x minutes. In the last week, you have noticed that when driving at 50 mph (miles per hour), you arrive home 4 minutes earlier than normal, and when driving at 40 mph, you arrive home 5 minutes earlier later than normal. If the distance between your office and your apartment is y miles, calculate x + y.

You might be interested in