Subjects algebra

Distance Time 0D7Cdc

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1. **State the problem:** We have a table showing Jerome's distance from the finish line over time in minutes. We want to understand the relationship between time and distance. 2. **Identify the pattern:** The distance decreases by 2 km every 11 minutes, starting at 10 km at time 0. 3. **Write the formula:** Distance $d$ as a function of time $t$ (in minutes) is linear and can be written as: $$d = d_0 - rt$$ where $d_0$ is the initial distance and $r$ is the rate of change of distance per minute. 4. **Calculate the rate $r$:** $$r = \frac{\text{change in distance}}{\text{change in time}} = \frac{10 - 8}{0 - 11} = \frac{2}{11}$$ Since distance decreases, rate is negative: $$r = -\frac{2}{11}$$ 5. **Write the distance function:** $$d = 10 - \frac{2}{11}t$$ 6. **Interpret the function:** At $t=0$, $d=10$ km, matching the table. At $t=55$ minutes: $$d = 10 - \frac{2}{11} \times 55 = 10 - 10 = 0$$ which matches the finish line. 7. **Answer part A:** At the start ($t=0$), Jerome is 10 km from the finish line. 8. **Answer part B:** The table uses kilometers, not miles, so Jerome is not 55 miles from the finish line at the start; this is incorrect. Final answers: - A) True, Jerome is 10 km from the finish line at the start. - B) False, the distance is in kilometers, not miles.