Problem
Tatum and Riley are both running along the same path. This graph represents their distances from the school, $D$, in kilometres, and their time spent running, $t$, in minutes. Distance from School vs. Time D 10 5 Tatum 0 5 10 15 20 25 30 Time (min) After how many minutes of running will Tatum and Riley be the same distance from the school? 3 minutes 6 minutes 20 minutes 30 minutes
Solution
Step 1 ：\(D_{Tatum} = \frac{1}{3}t\)
Step 2 ：\(D_{Riley} = \frac{1}{2}t\)
Step 3 ：Set \(D_{Tatum} = D_{Riley}\)
Step 4 ：\(\frac{1}{3}t = \frac{1}{2}t\)
Step 5 ：Subtract \(\frac{1}{3}t\) from both sides
Step 6 ：\(\frac{1}{6}t = 0\)
Step 7 ：Multiply both sides by 6
Step 8 ：\boxed{t = 0}\)
