The time needed to paint a fence varies directly with the length of the fence and inversely with the number of painters. If it takes five hours to paint 200 feet of fence with three painters, how long will it take five painters to paint 500 feet of fence?

Calculate Rate: First, let's find the rate at which one painter can paint the fence. We use the formula: Time = (Length of fence × Number of painters) / Rate. Here, we know the time (5 hours), the length (200 feet), and the number of painters (3). So, we solve for Rate. Rate = (200 feet × 3 painters) / 5 hours = 120 feet per hour per painter. Calculate Time: Now, we need to calculate the time it will take for five painters to paint 500 feet of fence using the rate we found. We rearrange the formula to solve for Time: Time = (Length of fence × Number of painters) / Rate. Time = (500 feet × 5 painters) / 120 feet per hour per painter = 20.83 hours.

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The time needed to paint a fence varies directly with the length of the fence and inversely with the number of painters. If it takes five hours to paint 200 feet of fence with three painters, how long will it take five painters to paint 500 feet of fence?

The time needed to paint a fence varies directly with the length of the fence and inversely with the number of painters. If it takes $5$ hours to paint $200$ feet of fence with $3$ painters, how long will it take $5$ painters to paint $500$ feet of fence?

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Q. The time needed to paint a fence varies directly with the length of the fence and inversely with the number of painters. If it takes

5

hours to paint

200

feet of fence with

3

painters, how long will it take

5

painters to paint

500

feet of fence?

Calculate Rate: First, let's find the rate at which one painter can paint the fence. We use the formula: $\text{Time} = \frac{\text{Length of fence} \times \text{Number of painters}}{\text{Rate}}$ . Here, we know the time ( $5$ hours), the length ( $200$ feet), and the number of painters ( $3$ ). So, we solve for Rate. $\newline$ Rate = $\frac{200 \text{ feet} \times 3 \text{ painters}}{5 \text{ hours}} = 120 \text{ feet per hour per painter}$ .
Calculate Time: Now, we need to calculate the time it will take for five painters to paint $500$ feet of fence using the rate we found. We rearrange the formula to solve for Time: $\text{Time} = (\text{Length of fence} \times \text{Number of painters}) / \text{Rate}$ . $\newline$ $\text{Time} = (500 \text{ feet} \times 5 \text{ painters}) / 120 \text{ feet per hour per painter} = 20.83 \text{ hours}.$