Candace leaves her house and starts jogging at a pace of 480 feet per minute. Five minutes later, her brother runs after her at a pace of 660 feet per minute. If both of them continue at these speeds, how long will it take her brother to catch up? Here is the equation that models the problem, where t represents time in hours.
480t = 660(t – 112)
working in minutes (like the speeds) ... 480t = 660(t – 5)
3300 = 180 t
To solve the equation 480t = 660(t – 112) for t, you can follow these steps:
Step 1: Distribute the 660 on the right side of the equation:
480t = 660t – 73920
Step 2: Move the 480t term to the right side by subtracting it from both sides of the equation:
480t - 480t = 660t - 480t - 73920
0 = 180t - 73920
Step 3: Move the constant term to the left side by adding 73920 to both sides of the equation:
0 + 73920 = 180t - 73920 + 73920
73920 = 180t
Step 4: Divide both sides of the equation by 180 to isolate t:
73920/180 = (180t)/180
410.67 = t
So, it will take her brother approximately 410.67 minutes to catch up to Candace.
To solve the equation and find the time it takes for Candace's brother to catch up to her, we need to simplify and solve for t.
Let's go step by step:
1. Distribute 660 to the terms inside the parentheses:
480t = 660t - 73,920
2. Combine like terms by subtracting 480t from both sides of the equation:
0 = 180t - 73,920
3. Add 73,920 to both sides to isolate the term with t:
73,920 = 180t
4. Divide both sides of the equation by 180 to solve for t:
t = 73,920 / 180
5. Calculate the value of t:
t ≈ 411.78
Hence, it will take Candace's brother approximately 411.78 minutes to catch up to her.