A bridge to nowhere
This is another cache in the series that requires
some mathematical problem solving to find the solution. The
co-ordinates at the top of the page give the general location of
the cache. The cache is on the Flitch way cycle and walking route.
There are many places that you can join the Flitch way, from
footpaths to ramps at most road crossings. You choose your own
starting point. There are quite a few other caches along the same
path. But now to the problem. This one is an A-level Standard
question.
Fred takes his geocaching very seriously. He has
found out that the time time it takes him to complete a cache from
arriving at the parking place, finding the cache and returning to
his car, can be modeled by a probability density function given
by:
Where t is the time in minutes that he takes to do
a cache and k is a constant.
By integrating this function he can find the
probability of finding a cache in a certain time. Fred knows that
he completes 50% of his caches in 56 minutes and 13.8 seconds.
How long does it take Fred to complete 20% of his caches? This
time is the Easting of the co-ordinates of the cache in
minutes.
How long does it take Fred to complete 47.328% of
his caches? This time is the minutes part of the Northing of the
location of the cache. The Northing is given by 51 degrees and X
minutes. X is the number you just found.
If you get stuck you can e-mail me for help or to
check your answers. The final cache location is ticky to get to
hence the terrain rating. Please take care.