Speed question

Question

The mile meter of a car misses every eleventh mile being traveled. After a certain time, the meter shows that 1251 miles were traveled. How many miles were actually traveled?

Answer 1

The "mile meter" of a car is called an odometer.

If the odometer shows 10 miles, the car has actually travelled 10 or 11 miles (the odometer doesn’t advance). If the odometer shows 20 miles, the car has actually travelled 21 or 22 miles. ... This is (11/10)*(reading).

If the odometer shows 1251 miles, then the car has actually travelled (11/10)*(1251)=1376.1 miles [but be careful!].
"The mile meter of a car misses every eleventh mile being travelled." This means that it shows:
           1 2 3 4 5 6 7 8 9 10 10 11 12 13 14 ...
  for     1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ...

But 1375/11 = 125   [1375 is a multiple of 11, so the "miss" occurs here]

This means that the odometer shows:

               1249  1250  1250  1251  1252  1253  ...

   for        1373  1374  1375  1376  1377  1378 ...

So, the odometer reads 1250 when the distance is 1374 and it continues to read 1250 when the distance is 1375, then it increments again to 1251 when the distance is 1376.