The Pancho Villa Trip
We have three numbers, one in each milestone:
xy yx x0y
We can see that x must be less than y, because the distance in the second landmark must be greater than the distance in the first.
We can also conclude that x = 1, because the distance between each landmark is a 2-digit number, and the sum of two 2-digit numbers will never result in a value greater than 198.
Then we can write the three numbers as follows:
10 + y 10.y + 1 100 + y
We want to know the speed that Pancho Villa walks.
Let's call this speed z. Then we can assemble the following equations:
z = (10y + 1) - (10 + y) and z = (100 + y) - (10y + 1)
Overriding the value of z In the second equation we have:
(10y + 1) - (10 + y) = (100 + y) - (10y + 1)
9y-9 = 99-9y
18y = 108
y = 6
Now just put this value in the first equation to find the z:
z = (10.6 + 1) - (10 + 6)
z = 60 + 1-10-6
z = 45
So Pancho Villa walked at a speed of 45km / h.
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