On Sept. 1, we wish to go to Zhangye directly from Beijing.

Well, there is no direct high speed train between these two cities.
The schedules of normal speed trains are 10:00, 10:55 and 15:15.
The ticket fare of soft sleeper is about CNY625 and hard sleeper is about CNY407.
You can check the detailed info on this website by yourself.

Thank you for letting me know there is only normal speed train service from Beijing to Zhangye.
1. Please tell me how long does it take.
2. What is our other option? Looks like we have to fly from Beijing to Lanzhou to connect a train to Zhangye, or to
Xining to connect a bus to Zhangye.

Kindly advise.

Peter Leung
Los Angeles

The normal speed train takes around one day long.
Or like you said, you can take a plan from Beijing to Lanzhou first. The duration is about 3 hours.
Then take a high speed train from Lanzhou West Railway Station to get to ZY West Railway Station. It also takes around 3 hours. :-)

It might be cheaper to fly