Notice that the galactic distance versus velocity data fall along straight lines. This means that speed (v) and distance (r) are linearly related:

r = (some quantity)v.

The quantity that multiplies v must have units of time in order for the left side of the equation to have units of distance. The equation above is saying nothing more than

distance = (velocity)(time).

So a naive interpretation of the graphs is that all of the galaxies were created at the same time and have been traveling for the same amount of time, with the faster objects obviously traveling farther than the slower objects. If that is true, then we could get the age of the universe by finding out how long the galaxies have been traveling. This is easy; just solve the above equation for time:

time = (distance)/(velocity),

where the best value for this quantity is just 1/(slope) of one of the graphs.

But we must be careful about how the graphs are interpreted. After all, the data depend upon light which has been traveling millions of years before it reaches us. Much can happen to those galaxies in a few million years that we would know nothing about: during that time the galaxies could either speed up or slow down. Let's use the down-to-earth example of a car trip.

Suppose that a car's driver calls on a cell phone to tell you that they've traveled 120 mi, and that the current car speed is 40 mi/hr. If you assume that the car has traveled the entire 120 mi at 40 mi/hr, then you would say that the car has been traveling for a time = 120 mi/(40 mi/hr) = 3 hrs. But if in reality the car's speed has sometimes been as high as 70 mi/hr, it has taken the driver less than 3 hrs to travel the 120 miles.

Another possibility is that the driver reports after 120 mi that the current car speed is 40 mi/hr, but actually the car's speed has been lower for much of the trip. In that case, the car has obviously taken longer than 3 hrs to travel the 120 mi.

The time that we're discussing for the galaxies is represented by the symbol 1/H0 ; H0 is called the Hubble constant. Find the Hubble constant (the slope) for the most recent data, then discuss its meaning if (a) the galaxies have speeded up, or (b) the galaxies have slowed down since their light was emitted.