Question

Sarah is training for a marathon. Her personal trainer recommends that she runs every day and increases her distance by the exact same amount each day. If she ran 8 miles on the 3rd day and 35 miles on the 12th day, how far will she be able to run after 3 weeks?

Answer 1

If she ran 8 miles on the 3rd day and 35 miles on the 12th day, how far will she be able to run after 3 weeks?

Since Sarah increases her distance by the exact amount each day, the common difference is the same.

`\begin{gathered} T_3\text{ = a+2d = 8 }\ldots\ldots\ldots(1) \\ T_(12)\text{ = a+11d = 35}\ldots\ldots..(2) \\ \text{solve it using simultaneous equation} \\ \end{gathered}`
`\begin{gathered} U\sin g\text{ elimination method} \\ a+11d\text{ = 35} \\ \frac{a+2d=8}{9d\text{ = 27}} \\ \text{ d = }(27)/(9) \\ \text{ d = 3} \end{gathered}`
`\begin{gathered} a+2d\text{ = 8} \\ a+2(3)=8 \\ a\text{ +6 = 8} \\ a\text{ = 8-6} \\ a\text{ =2} \end{gathered}`
`\begin{gathered} 3\text{ w}eeks\text{ }\cong3(7)=21day\text{ } \\ T_(21)\text{ = a+20d} \\ T_{21\text{ }}\text{ = 2+20(3)} \\ T_(21)\text{ = 2+60} \\ T_(21)\text{ = 62} \end{gathered}`

Hence she will be able to run after 3 weeks = 62 miles