Let xkm/h represent the speed of the slower train
Since the faster train is 14km/h faster than the slower train, the speed of the faster train is (x+14)km/h
Since they meet after 6 hours, then it is the time taken to cover the distance 1800km
The formula for speed is
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]The distance travel by the slower train will be
[tex]\begin{gathered} \text{Speed}=\frac{\text{Distance}}{\text{Time}} \\ x=\frac{\text{Distance}}{6} \\ \text{Crossmultiply} \\ \text{Distance}=x\times6=6xkm \end{gathered}[/tex]The distance traveled by the slower train is 6xkm
The distance traveled by the faster train will be
[tex]\begin{gathered} \text{Speed}=\frac{\text{Distance}}{\text{Time}} \\ (x+14)=\frac{\text{Distance}}{6} \\ \text{Distance}=(x+14)\times6 \\ \text{Distance}=6(x+14)km_{} \end{gathered}[/tex]The distance traveled by the faster train is 6(x+14)km
The total distance will be
[tex]6x+6(x+14)=1800[/tex]Solve to find x
[tex]\begin{gathered} \text{Open the bracket} \\ 6x+6x+84=1800 \\ \text{Collect like terms} \\ 12x=1800-84 \\ 12x=1716 \\ \text{Divide both sides by 12} \\ \frac{12x}{12}=\frac{1716}{12} \\ x=143 \end{gathered}[/tex]Since, xkm/h is the speed of the slower train,
Hence, the rate of the slower train is
[tex]x=143\frac{km}{h}[/tex]Since, (x+14)km/h is the speed of the faster train,
Hence, the rate of the faster train is
[tex]\begin{gathered} (x+14)=143+14=157\frac{km}{h} \\ (x+14)=157\frac{km}{h} \end{gathered}[/tex]