Can someone explain how they came up with 10 billion years?
Not my explanation, I copied this. But it explains how the distances are calculated.
"The shortest method on the ladder used to measure the distance to stars is parallax. Parallax is the apparant change in position of an object when viewed from a different location. A simple demonstration is to hold a finger at arms length up in front of a distant object, then close one of your eyes. Your finger will appear to move relative to the distant object; if you open your eye and shut the other one, your finger will move again. To make a measurement of the parallax of a star, we can take a measurement of its position at a given time. Six months later, when the earth is on the other side of its orbit, we take another measurement of its position. By doing some trigonometry with the angle it has moved on the sky and the diameter of the Earth's orbit, we can work out the distance to the star. Parallax measurements can only be done for comparatively close stars, though. A star one parsec away will appear to move by 1/3600 of a degree over six months (i.e. one parallax second) - but the nearest star to us is 1.3 parsec away. To make parallax measurements to more distant stars requires very precise measurements of their position.
To make measurements to more distant stars, we need to use methods that depend on their brightness. Light obeys an inverse-square law, where the brightness decreases by the square of the increase in distance. If we have two objects of identical brightness, one a given distance away and one twice as far away, the object that is twice as far away will appear a quarter as bright. To use this, we need 'standard candles', objects that will have a consistent brightness no matter the distance.
The standard candle that is most useful at distances within our galaxy are cepheid variables. These are variable stars which have a defined relationship between their brightness and the time it takes for their variability to cycle. By measuring the change in brightness of a cepheid variable, we can work out how bright it should appear compared to other cepheids. We can then use parallax methods to measure the distance to nearby cepheids, which lets us work out bright they actually are. We can then use this to measure the distances to more distant cepheids and the stars around them.
To measure the distance to nearby galaxies, we can use Type Ia supernovae. These occur when a white dwarf sucks up enough gas (probably from another star it's orbiting) to reach 1.4 times the mass of the sun. At this point, the forces that hold the white dwarf together are overcome by gravity, and a supernova occurs as the star collapses. Because these always occur when the white dwarf reaches the 1.4 solar mass limit (the Chandrasekhar mass), they have a consistent brightness. This makes them very useful as standard candles. Other useful standard candles include RR-Lyrae variables (another class of variable stars), the Tully-Fisher relation (which links the luminosity and rotation velocity of spiral galaxies) and the Faber-Jackson relation (which links the luminosity and velocity distribution of stars in elliptical galaxies).
To measure the distance to distant galaxies, we can use Hubble's law. This relates the speed at which a galaxy appears to move away from us due to the expansion of space to the distance. To measure the speed of these galaxies, we measure their redshift, the amount by which the light from the galaxy has moved towards the red end of the spectrum due to the Doppler effect. This can then be turned back into a velocity, which can then be used to measure the distance to the galaxy."
Now, after all that we can use distance to figure age. Obviously, if a galaxy is 4 billion light years away, then it's gotta be at least 4 billion years old, since it's light took 4 billion years to reach us. Except (and this is the cool part) because the light took 4 billion years to reach us, we're seeing what it looked like 4 billion years ago, not what it looks like today. That object may not even exist today.