Question

working alone, john can oil the lanes in a bowling alley in nine hours. one day his friend ted helped him and it only took 4.74 hours. how long would it take ted to do it alone? hours = 19

Explanation:

Step1: Calculate work - rates

Let the work - rate of John be $r_J$ and the work - rate of Ted be $r_T$. The work $W$ of oiling the lanes is considered as 1 unit. Since John can do the work in 9 hours, $r_J=\frac{1}{9}$ of the work per hour. Let the time it takes Ted to do the work alone be $t$ hours, so $r_T = \frac{1}{t}$ of the work per hour. When they work together, their combined work - rate $r = r_J+r_T$, and they complete the work in 4.74 hours. So $r=\frac{1}{4.74}$ of the work per hour.

Step2: Set up the equation

We know that $r = r_J+r_T$. Substituting the values of $r$, $r_J$, and $r_T$ into the equation, we get $\frac{1}{4.74}=\frac{1}{9}+\frac{1}{t}$.

Step3: Solve for $t$

First, rewrite the equation as $\frac{1}{t}=\frac{1}{4.74}-\frac{1}{9}$. Find a common denominator, which is $4.74\times9 = 42.66$. Then $\frac{1}{t}=\frac{9 - 4.74}{42.66}=\frac{4.26}{42.66}$. Cross - multiply to get $4.26t=42.66$. Solving for $t$, we have $t=\frac{42.66}{4.26}\approx10$ hours.

Answer:

10 hours