Question

14.

Jeremy can build a model airplane in 5 hours less time than his brother. Working together they need 6 hours to build the plane. How long would
it take Jeremy to build the model airplane working alone?

Answer 1

Let's assume Jeremy's brother can build the model airplane in x hours. Then we know that Jeremy can build it in x-5 hours.

To work together, their combined work rate is the sum of their individual work rates. So we have:

1/x + 1/(x-5) = 1/6

We can solve for x, the number of hours it would take Jeremy's brother to build the model airplane alone:

6(x)(x-5) = x(x-5) + x(6)

Simplifying this expression, we get:

6x^2 - 30x = x^2 - 5x + 6x

5x^2 - 31x = 0

x = 31/5

So it would take Jeremy's brother 6 hours and 12 minutes to build the model airplane alone.

Since we know Jeremy can build it in 5 hours less time, it would take him 31/5 - 5 = 6 1/5 - 5 = 1 1/5 or 1 hour and 12 minutes to build the model airplane working alone.