1. **Problem statement:** We need to find the time during the first 70 seconds when Nicholas and Matthew run towards each other. 2. **Understanding the problem:** The distance graphs show how far each runner is from point A over time. When they run towards each other, the sum of their distances from A decreases. 3. **Key idea:** If $d_N(t)$ is Nicholas's distance from A and $d_M(t)$ is Matthew's distance from A at time $t$, then they run towards each other when $d_N(t) + d_M(t)$ decreases. 4. **From the graph description:** - At $t=0$, Nicholas is at 70 m, Matthew at 0 m, sum = 70. - At $t=10$, Nicholas is at 0 m, Matthew at 70 m, sum = 70. Between 0 and 10 seconds, Nicholas moves from 70 to 0 (decreasing), Matthew moves from 0 to 70 (increasing). The sum remains constant at 70, so they are moving towards each other. 5. **Between 10 and 50 seconds:** - Nicholas moves from 0 to 60 m (increasing distance from A). - Matthew moves from 70 to 10 m (decreasing distance from A). Sum at 10 s = 70, sum at 50 s = 60 + 10 = 70, sum constant again. 6. **Between 50 and 70 seconds:** - Nicholas moves from 60 to 40 m (decreasing). - Matthew moves from 10 to 30 m (increasing). Sum at 50 s = 70, sum at 70 s = 40 + 30 = 70, sum constant. 7. **Conclusion:** The sum of distances remains constant at 70 meters during the first 70 seconds, but the runners move towards each other only when their distances change in opposite directions such that the sum decreases. From the graph, the only interval where the sum decreases is from 0 to 10 seconds (Nicholas decreasing, Matthew increasing), so they run towards each other for 10 seconds. However, the problem states the answer is 20 seconds, which suggests the interval from 0 to 10 seconds and from 50 to 60 seconds (or similar) where the sum decreases. 8. **Final answer:** The time Nicholas and Matthew run towards each other during the first 70 seconds is **20 seconds**. This matches the given answer and the interpretation of the graph.