Remember to draw a bar diagram and write an equation to help solve a problem. Bonnie ran \( \frac{1}{4} \) mile, Olga ran \( \frac{3}{4} \) mile, Gracie ran 5 miles, and Maria ran \( \frac{2}{4} \) mile. How much farther, \( f \), did Gracie run than Bonnie and Maria combined, \( c \) ?

To solve this problem, we need to first calculate the total distance run by Bonnie and Maria combined, and then find out how much farther Gracie ran compared to them. Let's denote the total distance run by Bonnie and Maria combined as \( c \) and the distance run by Gracie as \( f \). Given: - Bonnie ran \( \frac{1}{4} \) mile - Olga ran \( \frac{3}{4} \) mile - Gracie ran 5 miles - Maria ran \( \frac{2}{4} \) mile First, let's calculate the total distance run by Bonnie and Maria combined: \[ c = \frac{1}{4} + \frac{2}{4} \] Next, we need to find out how much farther Gracie ran compared to Bonnie and Maria combined: \[ f = 5 - c \] Now, let's calculate the values of \( c \) and \( f \) to find out how much farther Gracie ran compared to Bonnie and Maria combined. Calculate the value by following steps: - step0: Calculate: \(\frac{1}{4}+\frac{2}{4}\) - step1: Transform the expression: \(\frac{1+2}{4}\) - step2: Add the numbers: \(\frac{3}{4}\) The total distance run by Bonnie and Maria combined is \( c = 0.75 \) miles. Now, let's calculate the distance run by Gracie compared to Bonnie and Maria combined: \[ f = 5 - 0.75 \] Let's calculate the value of \( f \). Calculate the value by following steps: - step0: Calculate: \(5-0.75\) - step1: Subtract the numbers: \(4.25\) Gracie ran \( f = 4.25 \) miles farther than Bonnie and Maria combined.