Answer: On the first day, Shelly rode 10 miles on first day.
On the second day, Shelly rode 8 miles.
On the third day, Shelly rode 12 miles.
Step-by-step explanation:
Let x = distance rod eon first day.
Shelly rode her bike a total of 30 miles over a three-day period.
Then as per given,
Distance rode on second day = [tex]\dfrac45x[/tex]
Distance rode on third day [tex]=\dfrac32\times\text{ Distance rode on second day}[/tex]
[tex]=\dfrac32\times\dfrac45x=\dfrac{6}{5}x[/tex]
Total distance rode = [tex]x+\dfrac45 x+\dfrac65x=30[/tex]
[tex]\Rightarrow\ \dfrac{5x+4x+6x}{5}=30\\\\\Rightarrow\ \dfrac{15x}{5}=30\\\\\Rightarrow\ 3x=30\\\\\Rightarrow\ x=\dfrac{30}{3}\\\\\Rightarrow\ x=10[/tex]
Hence, She rode 10 miles on first day.
Distance rode on second day = [tex]\dfrac45\times10=4\times2=8\text{ miles}[/tex]
Distance rode on third day [tex]=\dfrac{3}{2}\times8=3\times4=12\text{ miles}[/tex]
