Messenger 3117

One messenger went 7 miles every day. When he had gone 64 miles, his master sent another messenger after him, who went 9 miles daily. How many days did the second messenger catch up with the first messenger?

Correct answer:

x =  32 d

Step-by-step explanation:

$$\begin{gathered} v_1=7\text{min/d} \\ {v}_2=9\text{min/d} \\ {s}_1=64\text{mil} \\ {t}_1=s_1/v_1=64/7=\frac{64}{7}\doteq 9.1429\text{d} \\ {v}_1\cdot (x+t_1)=v_2\cdot x \\ 7\cdot (x+9.1428571428571)=9\cdot x \\ 2x=64 \\ x=\frac{64}{2}=32 \\ x=32=32\text{d} \end{gathered}$$

Try another example