Mathematical_Recreations-Kraitchik-2e

38 Mathematical Recreations
chased is equal to the number of his or her purchases. Arthur
has bought 23 more articles than Barbara, and Bernard has
bought 11 more than Ann. Each husband has spent $63
more than his wife. Who is the husband of whom?
Answer: Arthur and Cynthia, Bernard and Barbara,
Charles and Ann.
44. Every day at noon a ship leaves New York for Lisbon,
and at the same instant a ship leaves Lisbon for New York.
Each trip lasts exactly 192 hours, or 8 days. How many ships
from Lisbon will each ship from New York meet?
Solution: A ship leaving New York on the 15th will meet
at the dock the ship which left Lisbon on the 7th, and will
meet all the west-bound ships thereafter until it meets in the
dock at Lisbon the ship which is leaving for New York on the
23rd. Thus the east-bound ship meets 17 west-bound ships.
The solution may be found graphically with ease.
46. A double-track trolley line runs between two stations
6 miles apart. From each station cars set out for the other
station every 3 minutes and proceed at uniform speed. A
pedestrian leaves one station just as one car is arriving and
another leaving. He walks beside the right-of-way at constant
speed until he reaches the other station just as one car
is arriving and another leaving. Including these 4, he saw
62 cars on his way, 19 going in the same direction and 43 in
the opposite direction. What was his speed, and what was
the speed of the cars? Answer: 4 and 10 miles per hour.
46. Stations A and Bare 120 miles apart on a single-track
railroad. At the same instant that a train leaves A for B at
25 miles an hour, a train leaves B for A at 15 miles an hour.
Just as the first train leaves A, a fly flies from the front of the
engine straight toward the other train at 100 miles an hour.
On meeting the second train it immediately turns back and
flies straight for the first train. So it continues to fly back