Alone, It Takes Khalil 10 Hours To Complete A One-Hour Long Presentation. It Takes Teddy 8 Hours To Complete A One-Hour Long Presentation. Using A Rational equation, which of the following correctly calculates how long it would take them to complete a one-hour long presentation if they worked together?

1 answer

To solve the problem using a rational equation, we can assign variables to represent the time it takes each person to complete a one-hour presentation. Let's assign "x" to Khalil's time and "y" to Teddy's time.

Based on the given information, we know that Khalil takes 10 hours to complete a one-hour presentation, so his rate of work would be 1/10 (1 hour completed / 10 hours worked). Similarly, Teddy takes 8 hours to complete a one-hour presentation, so his rate of work would be 1/8 (1 hour completed / 8 hours worked).

When they work together, their rates of work will add up, so we can set up the following equation:

1/x + 1/y = 1/t

Where "t" represents the time it would take them together to complete a one-hour presentation.

Substituting the rates of work, we have:

1/10 + 1/8 = 1/t

To simplify this equation, we need to find a common denominator, which is 40 in this case:

4/40 + 5/40 = 1/t

Combining the fractions:

9/40 = 1/t

To solve for "t", we can cross-multiply:

9t = 40

Dividing both sides by 9:

t = 40/9

Therefore, when Khalil and Teddy work together, it would take them approximately 4.44 hours to complete a one-hour long presentation.