22 Arithmetic & Algebraic Problemshour when Baxter went after him along the same road. Baxter's dog started
at the same time as his master and ran uniformly forwards and backwards
between him and Anderson until the two men were together. Anderson's
speed is two, Baxter's four, and the dog's ten miles an hour. How far had the
dog run when Baxter overtook Anderson?
My correspondent in Italy who sends me this is an exact man, and he says,
"Neglect length of dog and time spent in turning." I will merely add, neglect
also the dog's name and the day of the month.- THE RUNNER'S REFRESHMENT
A man runs n times round a circular track whose radius is t miles. He drinks
s quarts of beer for every mile that he runs. Prove that he will only need one
quart!76. EXPLORING THE DESERT
Nine travellers, each possessing a car, meet on the eastern edge of a desert.
They wish to explore the interior, always going due west. Each car can travel
forty miles on the contents of the engine tank, which holds a gallon of fuel,
and each can carry nine extra gallon cans of fuel and no more. Unopened
cans can alone be transferred from car to car. What is the greatest distance
at which they can enter the desert without making any depots of fuel for the
return journey?- EXPLORING MOUNT NEVEREST
Professor Walkingholme, one of the exploring party, was allotted the spe-
cial task of making a complete circuit of the base of the mountain at a certain
level. The circuit was exactly a hundred miles in length and he had to do it
all alone on foot. He could walk twenty miles a day, but he could only carry
rations for two days at a time, the rations for each day being packed in sealed
boxes for convenience in dumping. He walked his full twenty miles every day
and consumed one day's ration as he walked. What is the shortest time
in which he could complete the circuit?
This simple question will be found to form one of the most fascinating