Two identical balls roll across the top of a table on parallel paths. One of the balls has to roll down into and up out of a dip in the table. The other ball rolls on the flat all the time. Which ball gets to the far side of the table first, and why?.

(In reply to

Second attempt - physics based solution by Kenny M)

should'nt the average speed be

.5[v0 + sqrt(v0^2 + 2*g*h)] and not v0 + .5*sqrt(v0^2 + 2*g*h)

also the relation between h and (theta) tan(theta)= h/(v0*t1/2)

i could not work it out but the equation may be reduced a little by it.