Three trucks

There are places A and Y, three trucks, B, C, and D, respectively. Truck B is 60 km/h, C is 40 km/h and D is 80 km/h. Trucks B and C start at place A while D starts at Y. After D and B meet, two hours later, will D meet C. What is the distance between places A and Y?

Final Answer:

x =  1680 km

Step-by-step explanation:

$$\begin{gathered} B=60\text{km/h} \\ C=40\text{km/h} \\ D=80\text{km/h} \\ T=2\text{h} \\ x=(B+D)\cdot t_1 \\ x=(C+D)\cdot t_2 \\ {t}_2=t_1+T \\ (B+D)\cdot t_1=(C+D)\cdot t_2 \\ (B+D)\cdot t_1=(C+D)\cdot (t_1+T) \\ (60+80)\cdot t_1=(40+80)\cdot (t_1+2) \\ 20t_1=240 \\ {t}_1=\frac{240}{20}=12 \\ {t}_1=12 \\ {t}_2=t_1+T=12+2=14\text{h} \\ x=(B+D)\cdot t_1=(60+80)\cdot 12=1680=1680\text{km} \\ \text{ Verifying Solution: } \\ {x}_2=(C+D)\cdot t_2=(40+80)\cdot 14=1680\text{km} \end{gathered}$$

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