The speeds of four cars are 2u, 3u, 4u and xu and the time taken by them to cover the same distance is xt, 4t, 3t and 2t respectively, where x, u, t are real numbers. What is the value of x ?

Since distance is the same for all cars, speed × time = constant. So 2u·xt = 3u·4t = 4u·3t = xu·2t. From 2u·xt = 3u·4t, we get 2xt = 12t, so x = 6. Checking with xu·2t = 12ut gives 2xut = 12ut, so x = 6. But also 2u·xt must equal xu·2t, which gives 2xut = 2xut (always true). Using 3u·4t = 12ut as the common distance, 2u·xt = 12ut gives x = 6. Hence x = 6.