"In the illustration we have a sketch of Sir Edwyn de Tudor going to rescue his lady-love, the fair Isabella, who was held a captive by a neighboring wicked baron. Sir Edwyn calculated that if he rode fifteen miles an hour he would arrive at the castle an hour too soon, while if he rode ten miles an hour he would get there just an hour too late. Now, it was of the first importance that he should arrive at the exact time appointed, in order that the rescue that he had planned should be a success, and the time of the tryst was five o'clock, when the captive lady would be taking her afternoon tea. The puzzle is to discover exactly how far Sir Edwyn de Tudor had to ride."
from Henry Dudeney's
Amusements in Mathematics
60 miles.
ReplyDeleteAt fifteen mph for y amount of time he would arrive at the same place as he would going ten mph for x amount of time.
So 15y = 10x or y = (2/3)x
We also know that the amount of time x is two hours longer than the amount of time y.
So x - y = 2
combining the two we get:
(1/3)x = 2 or x = 6
y = 4
and 15y = 10x = 60.
So 60 miles.
Spot on. Congrats.
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