Serway & Jewett — Angular Momentum: Problem 35

We have all complained that there aren’t enough hours in a day. In an attempt to fix that, suppose all the people in the world line up at the equator and all start running east at $2.50\text{ m/s}$ relative to the surface of the Earth. By how much does the length of a day increase? Assume the world population to be $7.00 \times 10^9$ people with an average mass of $55.0\text{ kg}$ each and the Earth to be a solid homogeneous sphere. In addition, depending on the details of your solution, you may need to use the approximation $1/(1 - x) \approx 1 + x$ for small $x$.