Therese and Rob*
A couple of university students once told of how they ended up in a self-imposed tie-and-ride time-trial.
It seemed they both needed to sign an agreement by a certain deadline to get into some low-cost rental accommodation. Without money for even bus-fare (they were living on APR scholarships), they decided to cycle out along Anzac Parade to meet with the landlord at the Waypoint 2 coordinates (labelled "Destination"). As they were both quite fit, they expected to arrive in plenty of time.
Unfortunately, one of the bicycles suffered catastrophic failure en route. So at the Waypoint 1 coordinates (labelled "Start"), they found themselves with just one functioning bicycle. However, they worked out that if they proceeded as in a tie-and-ride biathlon, they could still make the deadline.
Basically, one of them started running while the other rode the bicycle - as quickly as they could. Then a little way along, the rider tied (or locked, it is Sydney!) the bicycle by the road and continued on foot. The runner, on reaching the same point, unlocked the bicycle and cycled the rest of the journey.
They calculated the optimum location en route to leave the bicycle so as to arrive at their destination in the least possible time.
Their Ride
The table shows Therese and Rob's cycling and running speeds. Therese cycled first.
|
Speed (kph)
|
Cycling
|
Running
|
|
Therese
|
42
|
9
|
|
Rob
|
21
|
18
|
Their strategy worked and they both arrived at the destination in time to sign the deed (and are now cozily sharing a garage in the Eastern Suburbs with three other postgrads).
* Not their real names. In fact, this entire event probably never happened. (So please call off your lawyers, Therese and Rob.)
The Cache
In the frantic rush, they dropped one of the keys for the bike lock. Your geo-quest is to find the key. They are certain it is where the bicycle was locked en route.
For calculations, assume that all distances are straight-line distances from "Start". Keep in mind that the deadline is based on both Therese and Rob completing signing the deed. That is, the time is based on the arrival of the second of the two.
The cache is 15 metres due West from the side of the road.
A trackable Puzzle ? geo-pin awaits the FTFinder.
Congratulations to the irrepressibly determined marj01 on the FTF and deservedly acquiring the trackable Puzzle ? geo-pin.