Given that train travels eight hundred fifty miles in six hours.
Then speed of the train is given by formula
![Speed = (distance)/(time)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/rl2slxpqzezz5ccac8vjtp5hxuwva0whz0.png)
miles per hour
Now we have to find time when train travels five thousand one hundred miles.
so plug the value of speed and distance in above formula
![Speed = (distance)/(time)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/rl2slxpqzezz5ccac8vjtp5hxuwva0whz0.png)
![(850)/(6) = (5100)/(time)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/ycoz7rij2c5ipbx65cqxnrzozrm8rpd9i1.png)
![(850)/(6) = (5100)/(time)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/ycoz7rij2c5ipbx65cqxnrzozrm8rpd9i1.png)
850(time)=5100*6
850(time)=30600
time = \frac{30600}{850}
time = 36
Hence final answer is 36 hours.