Average speed

Let each "equal distance" as L.

The time taken for each "equal distance" is calculated by time = (distance)/(speed) = $\dfrac L{600}, \dfrac L{750}, \cdots, \dfrac L{825}$.

Average speed = (distance)/(time) = $\dfrac{5L}{\dfrac L{600} + \dfrac L{750} + \dfrac L{800} + \dfrac L{650} + \dfrac L{825}} = \dfrac 5{\dfrac1{600} + \dfrac 1{750} + \dfrac1{800} + \dfrac1{650} + \dfrac1{825}}$.

Now you can use a calculator to get the required average speed.