up to speed vs at their speed

Some examples from the web:

• I'd like to be brought up to speed as quickly as possible.
• Your men got me up to speed.
• I think we're all up to speed.
• Okay, now we're all up to speed.
• Pratt's up to speed on my stuff.
• I brought Tyler up to speed on the Irish.
• Who can get him up to speed on Felton Securities.
• I thought you were up to speed.
• Vince is already up to speed on this.
• Detective Ryan brought me up to speed on things.
• Thank you, Buzz, for bringing me up to speed.
• Someone needs to keep me up to speed on him.
• Nelson and Raven brought me up to speed.
• Smoke alarm working, fan back up to speed.
• Get him up to speed on our aid programme to Colombia.
• We got to get you up to speed, G.J.
• Your brother's brought me up to speed on your struggle.
• Just get him up to speed, Doc.
• I thought everyone here was up to speed.
• Bring the engines up to speed.

Some examples from the web:

• We must stay close to the people, move at their speed and stay orderly to stay productive.
• They saw something shoot by, moving at approximately twice their speed.
• At their current speed, they will arrive within minutes.
• 22 minutes at their current speed.
• at their different speeds (s)
• At their current speed, sir the entities will intercept us in... ten minutes, 31 seconds.
• In both cases, it shall be possible for interoperable rolling stock to be worked at their maximum speed (if allowed by the infrastructure) with sufficient acceleration margins (as specified in the following paragraphs).
• These flying saucers have come from Mars and at their current course and speed will enter Earth's orbit in 16 hours.
• All states, and developing countries in particular, must be accorded the right to industrialise themselves at a speed of their own choosing, which means that they must also be allowed to protect vulnerable industries.
• The engine and all attachments shall be running at their respective rated speeds in the idling mode
• Calls on the Commission and Council to maintain the European Union's firm commitment to a negotiated settlement with a view to ending partition of the island, and to use all appropriate instruments at their disposal to speed up the process;
• Well, clearly, your restorative powers are not renowned for their speed.
• I'm talking about matching their speed.
• Their speed makes them very stable.
• Two ex-governors have her number on their speed dial.
• Particles have their speeds reversed, then the changes - found a measurable effect.
• Particles have their speeds reversed, then the changes - found a measurable effect.
• Their speed was in excess of 2,000 knots.
• And they can increase their speed by up to three times when they are tense.
• Or that we cannot enter their speed of time and hope to live.