The formula you showed is EXACTLY the one I used to solve this, with the 60's and D's all cancelling out.
After doing that, I realized that the formula could be simpler (although obviously equivalent) if the variable we introduced to be later cancelled out was time rather than distance. And solving for a speed multiplier rather than a speed keeps the mph vs minutes complication out of the formula.
t-t/m = t/m+t/2
t is number of minutes that the moped climbed and
m is the ratio of motorcycle speed over moped speed on the climb.