Question

Andrew works out for 30 minutes every other day. If he spends \(35 \%\) of his workout time one day waiting for the weight rack, how many seconds of that day's workout did he spend waiting for the weight rack? A) 630 B) 35 C) 21 D) \(10.5\)

Short answer

The short version of the answer is: Andrew spent \(630\) seconds waiting for the weight rack. The correct answer is (A).

Step-by-step solution

Convert minutes to seconds

First, we need to convert Andrew's workout time from minutes to seconds. There are 60 seconds in one minute, so we can multiply his 30-minute workout by 60 seconds to convert it to seconds. \( 30~\text{minutes}\times 60~\text{seconds per minute} = 1800~\text{seconds} \)

Calculate the percentage of waiting time

Next, we need to find 35% of his workout time, which represents the time spent waiting for the weight rack. To do this, we multiply the total workout time (in seconds) by the percentage (in decimal form) of waiting. \(1800~\text{seconds} \times 0.35 = 630~\text{seconds} \)

Choose the correct answer

Now, we can compare our result to the answer choices: A) 630 (Correct) B) 35 C) 21 D) \(10.5\) So, the correct answer is \( \boxed{\text{(A)} ~630} \) seconds.

Key concepts

Percentage Calculation

Understanding how to calculate percentages is a key skill, especially in SAT math problems. To find the percentage of a given number, you need to multiply the number by the percentage converted into a decimal.
For instance, with Andrew's workout problem, we needed to find 35% of 1800 seconds, which is his total workout time.

• First, convert the percentage to a decimal by dividing it by 100. So, 35% becomes 0.35.
• Next, multiply the total time (1800 seconds) by the decimal value of the percentage, 0.35.
• This calculation gives you the result: 1800 seconds multiplied by 0.35 equals 630 seconds.

This means Andrew spends 630 seconds waiting for the weight rack. Learning this process will make similar percentage-based questions much simpler.

Time Conversion

Converting time from one unit to another is often necessary to solve word problems effectively. In Andrew’s case, his workout time is initially given in minutes, but the problem requires you to use seconds.
Here’s how you convert:

• Recognize that 1 minute equals 60 seconds.
• Multiply the number of minutes by 60 to convert to seconds.
• For Andrew's workout of 30 minutes, the conversion is 30 x 60 = 1800 seconds.

By converting his workout duration from minutes to seconds, calculations become straightforward, especially when combining with percentage calculations or other operations. Always ensure you’re using consistent units to avoid errors.

Problem Solving Steps

Approaching word problems systematically improves accuracy. Let's break down the steps as illustrated in Andrew's workout problem:

• Step 1: Identify the Information Provided - Recognize the total workout time he spends in minutes.
• Step 2: Convert Units if Necessary - Convert minutes to seconds to make further calculations easier.
• Step 3: Calculate the Required Value - Determine 35% of his workout time to identify the waiting time.
• Step 4: Compare and Conclude - Match your calculated result with the given options to find the correct answer.

These clear problem-solving steps help organize thoughts and ensure you accurately approach SAT math word problems, increasing your confidence and ability to find the right solution.