Respuesta :
Answer:
The distance from Kim’s home to the lake is 3000 meters.
Explanation:
Since the whole trip takes 35 minutes, and the speeds are in meter/second, first convert 35 minutes to seconds.
[tex]35\text{ minutes}=35\times60=2100\text{ seconds}[/tex][tex]\begin{gathered} Average\; \text{Speed}=\frac{\text{Distance}}{Time} \\ \implies\text{Dis}\tan ce=Average\; \text{Speed}\times Time \end{gathered}[/tex]• Her average speed while jogging = 5m/s
,• Her average speed while walking = 2m/s
• If the number of seconds spent walking = x seconds.
,• The number of seconds spent jogging = (2100-x) seconds.
• Distance covered walking = 2x
,• Distance covered jogging = 5(2100-x)
Since the distance walked and jogged is the same, we have that:
[tex]2x=5(2100-x)[/tex]We solve for x.
[tex]\begin{gathered} 2x=5(2100-x) \\ 2x=10500-5x \\ 2x+5x=10500 \\ 7x=10500 \\ x=\frac{10500}{7} \\ x=1500\text{ seconds} \end{gathered}[/tex]Substitute x=1500 to find the required distance.
[tex]\text{Distance covered walking=}2x=2\times1500=3000\text{ meters}[/tex]The distance from Kim’s home to the lake is 3000 meters.
