Minus' Solution to

Monty's Magic Mobile
Posted July 21 - 27, 1997

First Jeremy traveled 2 km/hour, then 5 km/hour, then 8 km/hour, then 11 km/hour, etc. The equation for the speed he traveled during the nth kilometer is: 2 + (n - 1)3 km/hour

During the 50th kilometer, he will be traveling at a speed of 2 + 49(3) = 149 km/hour.

The time for traveling the nth kilometer is 60/[2 + (n-1)3] in minutes.
Sum all of the times up for n from 1 to 50.
The result is approximately 105 minutes, so it takes Jeremy about 105 minutes to get to work at this rate.

Your Solutions

What can we say, Minus and the entire DEN gang was truly impressed with this week's star chef...HaL0N . It's not everyday we get solutions that are as well organized and carefully presented (in HTML!) as this. Two sharks fin up to HaL0N!

Solution to Monty's Magic Mobile Problem (brought to you by HaL0N):

First Part:
Just before Monty reaches work in his nifty magic mobile, he is traveling his 50th kilometer.  This being the case, Monty's speed increases 49 times (once for every kilometer he completed).  Since that increase is 3 km/hour every time, Monty's final speed is 147 km/hour (49 * 3 km/hour) more than the original speed; he was initially traveling at 2 km/hour.  Therefore his final speed is 149 km/hour (147 km/hour + 2 km/hour).

Second Part:
The total time it takes Monty to go to work in his Magic Mobile is the sum of the times it takes Monty to travel each kilometer.  Since he traveled 50 kilometers, there are 50 terms to add. If 'n' stands for the kilometer being traveled at a particular time, the total number of hours traveled is:

       1   1   1             1               1     1     1
       - + - + - + ... + ---------- + ... + --- + --- + ---
       2   5   8         2 + 3(n-1)         143   146   149

To find the total minutes, you multiply the resulting figure by 60 (roughly 104.6720353).  Rounded off to the nearest minute, the answer comes to 105 minutes.

Julia Robinson, of Methodist Ladies' College in Western Australia, only got the first part of this week's question correct. But her sweet, happy words really made our day. Gee, Julia, you really know how to wrap our grumpy shark around your little finger...
I worked out that Monty was travling at 149km/hr and it took him 55 minutes to get to work.

I just thought I would add that I really admire your maths problems. They really bring joy into my life.

Kudos to all our solution providers.

Minus was impressed by everyone who
attempted this week's challenge.
He knows they're not getting any easier!