Building Docker image succeeds on one machine but fails on another with `Could not resolve …`

I build my Docker image with the following command:

docker build -t my-tag:0.0.0 -f Dockerfile-staging .

On my machine (MBP in Thailand) it works.
On my colleagues machine (Ubuntu, China) it errors with:

Step 3/9 : RUN apt-get update &&     apt-get upgrade -y &&     apt-get install -y gcc &&     apt-get install -y git &&     apt-get install -y libcurl4 &&     apt-get install -y libpq-dev &&     apt-get install -y libssl-dev &&     apt-get install -y python3-dev &&     apt-get install -y librtmp-dev &&     apt-get install -y libcurl4-gnutls-dev &&     apt-get install -y libcurl4-openssl-dev &&     apt-get install -y postgresql-9.3 &&     apt-get install -y python-psycopg2
 ---> Running in f405a317507e
Err:1 http://deb.debian.org/debian buster InRelease
  Could not resolve 'debian.map.fastlydns.net' Could not resolve 'deb.debian.org'
Err:2 http://security.debian.org/debian-security buster/updates InRelease
  Could not resolve 'debian.map.fastlydns.net' Could not resolve 'security.debian.org'
Err:3 http://deb.debian.org/debian buster-updates InRelease
  Could not resolve 'debian.map.fastlydns.net' Could not resolve 'deb.debian.org'
Reading package lists...
W: Failed to fetch http://deb.debian.org/debian/dists/buster/InRelease  Could not resolve 'debian.map.fastlydns.net' Could not resolve 'deb.debian.org'
W: Failed to fetch http://security.debian.org/debian-security/dists/buster/updates/InRelease  Could not resolve 'debian.map.fastlydns.net' Could not resolve 'security.debian.org'
W: Failed to fetch http://deb.debian.org/debian/dists/buster-updates/InRelease  Could not resolve 'debian.map.fastlydns.net' Could not resolve 'deb.debian.org'
W: Some index files failed to download. They have been ignored, or old ones used instead.

Why is this happening? And how to fix?

Source: Docker Questions