Reaching week ten is quite a challenge, but it doesn't seem like it'll be that hard until right at the end. About halfway through week nine suddenly 6 or 7 stations will go into meltdown, and there is no way to plan ahead to ease traffic.
A few pointers, though:
As a guide I delivered roughly 2200 passengers by week 10.
I never went for the Shinkansen. Getting 2 other engines and relieving 2 lines instead of one always seemed like the best option.
If you need to pause the game, don't click the back button. Instead click on the clock in the top right and then the pause icon. This way your Metro map will stay on screen while paused and you can decide what to do next.
I hope this helps, but patience and perseverance are key. Best of luck!