Question

Jimmy can paint a classroom in 8 hours. His brother can do it in 6 hours. How long will it take them if they work together?

(Problem Solving involving Rational Equations)

Answer 1

Answer:

1/8 + 1/6=3+4/24

=7/24

they both take 7/24 hour

Answer 2

Answer:

Given that Jimmy takes 8 hours to paint a classroom and his brother takes 6 hours to do the same work.

To find how much time it will take for both of them to complete the work together.

Amount of work by Jimmy alone in 1 hour = 1/8th of the whole work.

Amount of work done by Jimmy alone in 1 hour = 1/6th of the whole work.

Let the total time taken by them to complete the work together be 'y' hours. Therefore total amount of work done by both of them in 1 hour is:

$\implies \dfrac{1}{y} = \dfrac{1}{8} + \dfrac{1}{6}\\\\\\\implies \dfrac{1}{y} = \dfrac{6 + 8}{8 \times 6} = \dfrac{14}{48}\\\\\\\implies \bf{\dfrac{1}{y} = \dfrac{7}{24}}\\\\\\\implies \boxed{ \bf{ y = \dfrac{24}{7}}}$

Therefore the total time taken to complete the work is:

⇒ y = 24/7 = 3.42 hours