Proportions 29. If the Work done to push a box is 50 Joules a certain distance, how much work is done to push the box if the distance gets divided by three?

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Let $$ W $$ represent the work done, defined by the formula

$$
W = F \times d,
$$

where $$ F $$ is the force and $$ d $$ is the distance.

1. Initially, we have

$$
W = 50 \text{ Joules}
$$

for some distance $$ d $$.

2. If the distance is reduced to $$ \frac{d}{3} $$, the new work done, $$ W_{\text{new}} $$, is

$$
W_{\text{new}} = F \times \frac{d}{3}.
$$

3. Since $$ F = \frac{W}{d} = \frac{50}{d} $$, substitute this into the equation for $$ W_{\text{new}} $$:

$$
W_{\text{new}} = \frac{50}{d} \times \frac{d}{3} = \frac{50}{3}.
$$

4. Thus, the new work done is

$$
\frac{50}{3} \text{ Joules},
$$

which is approximately $$ 16.67 $$ Joules.
The work done is $$ \frac{50}{3} $$ Joules, which is approximately 16.67 Joules.

Proportions 29. If the Work done to push a box is 50 Joules a certain distance, how much work is done to push the box if the distance gets divided by three?

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