Mr. X travels 13 km at a speed of 19 km/h, and 4 km at a speed of 2 km/h. What is the average speed during the entire journey?
We shall use the alligation formula. If a sample n1 has an average property of A1, and another sample n2 has an average property of A2, then the average property of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 2, A1 = 19, n1 = 13, n2 = 4, we have 13 × (A - 19) = 4 × (2 - A), from where we get A = 15 km/h. The "property" in the alligation formula could be speed, weight, price, etc.,