Question

1. it took khalid 90 minutes to complete 40 tasks. which of the following is an equivalent rate?

a. 10 tasks in 0.9 minutes
b. 10 tasks in 2.25 minutes
c. 10 tasks in 9 minutes
d. 10 tasks in 22.5 minutes

Explanation:

Step1: Find the rate for Khalid

The rate is tasks per minute or minutes per task. Let's find minutes per task. Khalid took 90 minutes for 40 tasks, so minutes per task is $\frac{90}{40}$ minutes per task. Simplify $\frac{90}{40}=\frac{9}{4} = 2.25$ minutes per 1 task? Wait, no, wait. Wait, 90 minutes for 40 tasks. So to find the time for 10 tasks, we can set up a proportion. Let $x$ be the time for 10 tasks. Then $\frac{90}{40}=\frac{x}{10}$. Cross - multiply: $40x=90\times10$. Then $x = \frac{90\times10}{40}=\frac{900}{40}=22.5$? Wait, no, that's not right. Wait, no, 90 minutes for 40 tasks. So the rate of tasks per minute is $\frac{40}{90}=\frac{4}{9}$ tasks per minute. Or minutes per task is $\frac{90}{40}=2.25$ minutes per task? Wait, no, 90 minutes for 40 tasks. So if we want to find the time for 10 tasks, since 40 tasks is 4 times 10 tasks, the time for 10 tasks should be 90 divided by 4. Because 40 tasks = 4×10 tasks. So time for 10 tasks = 90÷4 = 22.5 minutes? Wait, no, that can't be. Wait, let's check the options. Option D is 10 tasks in 22.5 minutes. Wait, let's do the proportion correctly. Let's set up the ratio of tasks to time. The original ratio is 40 tasks : 90 minutes. We want to find the time for 10 tasks. So $\frac{40}{90}=\frac{10}{x}$, where $x$ is the time for 10 tasks. Cross - multiply: $40x = 90\times10$. Then $x=\frac{900}{40}=22.5$ minutes. So 10 tasks take 22.5 minutes. So the equivalent rate is 10 tasks in 22.5 minutes.

Answer:

D. 10 tasks in 22.5 minutes