Friday Puzzler -- Mopeds and Motorcycles

Re: Friday Puzzler -- Mopeds and Motorcycles

Larry Barrett

I think the motorcycles are traveling twice as fast as the moped. Not sure how to prove this. I tried one case, assuming the hill was 18 miles long so that the moped took 60 minutes to reach the top. Then, assuming the motorcycles traveled at twice the speed, they would reach the top in 30 minutes. So if one leaves the starting point every 30 minutes then 30 will pass the moped when it reaches the top (the 30th will reach the top just as the moped does). When the moped goes back down at 36 mph it will reach the bottom in 30 minutes, and in those 30 minutes it will pass 30 motorcycles. QED (sort of).

:-(

Alex Y

Wrong answer, but very close on reasoning. Reconsider how many he

will pass on the way down.

Re: :-(

Larry Barrett

I assumed that the hill was empty when the moped started down. But there will be motorcycles already on the hill, plus those that will start up as the moped goes down.

I think the answer to the question is that the motorcycles travel at 4 times the speed of the moped (72 mph).

My equation that solves this is

(((D/M)x60) - ((D/S)x60)))=(((D/2M)x60 + ((D/S)x60)))

where D is the distance the moped travels,

M is the speed the moped travels,

S is the speed the motorcycles travel.

The left side is the number of motorcycles that pass the moped going up, the right side is the number of motorcycles that the moped passes going down. The '60' converts mph to mp minute.

Correct :-)

Another formula

Alex Y

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

Where

t is number of minutes that the moped climbed and

m is the ratio of motorcycle speed over moped speed on the climb.