The traveler passed the sixth part of the way and realized that he had 10 km to go. How long is the entire path?

To solve this problem, remember, in order to find the number by its part, expressed as a fraction, you need to divide this number by a fraction. Let’s calculate what part of the path is left for the traveler to pass.
1 – 1/6 = 6/6 – 1/6 = 5/6 part.
Knowing that 5/6 of the entire path is 10 kilometers, we calculate what the length of the entire path is equal to.
10: 5/6 = 10 * 6/5 = 60/5 = 12 kilometers.
To divide an ordinary fraction, the numerator of the dividend must be multiplied by the denominator of the divisor, and the denominator of the dividend must be multiplied by the numerator of the divisor.
Answer: 12 km.