I'm not aware of any ships that can cross oceans at the desired speed, which implies that only those who can fly over the atlantic / pacific oceans will survive. And then, fuel will be an issue -- that many airplanes trying to make the same trans-oceanic journey at the same time will be difficult.
So, many die stuck in traffic jams, trying to head west. Many on the western coasts, and in boats off of the western coasts, overtaken. Lots of airplanes that
go down in the middle of the ocean: they didn't start with enough fuel to make the full journey, and all the refueling spots have been used up by airplanes that got there faster.
And when those who cross the Atlantic from Europe and Africa get to North and South America, they won't be able to refuel to cross the continent and the Pacific, because the residents of the Americas will have used all the available resources in their own attempts to head west. Similarly, if the attack continues for more than a day, those from the Americas arriving in Asia will find that they have no way of traversing the continent at the required speed.
The only way to survive would be to be close enough to the poles to have considerably less distance to go, and on the ice caps, modes of transportation will be even more limited. And that solution only works if the attack stops after 24 hours -- if it's ongoing, those who survived by being close enough to the ice-caps to keep moving would starve.
In other words, in your scenario, humanity would be screwed.
What if they had time to plan and prepare? Well, I think we'd last a little longer, but not for long. There is no way around the fact that traveling around the globe in 24 hours, regardless of method, will require a LOT of fuel. We'd need to set up robotic fuel extraction, production, transportation, and refueling stations, so this work would continue while humans were elsewhere. This would also require global cooperation to be sustainable, and maintenance would be difficult. Ditto with food. Even if we have custom boats/planes/vehicles fitted with hydroponics labs, they will need a consistent supply of fertilizer in order to stay viable.
So, even with time to prepare, humanity would be screwed. I'm just not able to come up with a way that your scenario would be survivable. If it lasted only 24 hours, then there might be a few dozen survivors near the poles, and a few thousand from the Americas stranded in Asia and Australia. Longer? Everybody's dead, Dave.