if 10 machines can produce 500 items in 5 hours,how many hours will take if only 5 machines are used.​

Answer:Here's how to solve this problem: 1. Find the production rate of one machine:If 10 machines produce 500 items in 5 hours, then one machine produces 500 items / 10 machines = 50 items per 5 hours.This means one machine produces 50 items / 5 hours = 10 items per hour. 2. Calculate the total production time for 5 machines:If 5 machines produce 10 items per hour each, they produce a total of 5 machines * 10 items/hour/machine = 50 items per hour.To produce 500 items, it will take 500 items / 50 items/hour = 10 hours. Therefore, it will take 10 hours for 5 machines to produce 500 items.

Answered by alixzamarirapacon | 2024-10-17

SOLUTION:We let N be the number of machines and t be the time in hours.Step 1: Calculate the proportionality constant if t = 5 when N = 10.[tex]\begin{aligned} t & = \frac{k}{N} \\ k & = Nt \\ k & = (10)(5) \\ k & = 50 \end{aligned}[/tex]Step 2: Solve for t when N = 5.[tex]\begin{aligned} t & = \frac{k}{N} \\ t & = \frac{50}{5} \\ t & = \boxed{\text{10 hours}} \end{aligned}[/tex]Hence, 10 hours will be taken if only 5 machines are used.

Answered by GreatRedSpot | 2024-10-17