Distance and Time Quiz Set 011

If the distance between them is L, they meet after travelling L/2. Equating the times they travelled, $L/{2 × 4} = L/{2 × 8} + 1$. Solving for L we get L = 16 km.

Let the normal speed be x km/hr. We have been given $12/x$ - $12/{x + 2}$ = 3. This translates to the quadratic equation $3x^2 + 6x - 24 = 0$, which can be solved to obtain x = 2 as the answer. If you don't want to solve the equation, then you can put each option into this equation and check that way. But this trick will work only if all the options have some numerical value.

By the given problem, the time is same for both cases. If the total distance covered by him at 4km/h is x, then, $x/4 = {x + 10}/6$. Solving, we obtain x = 20 km.

Let the speed of the train be v km/h. Length of the train calculated with the data for the first man = $(v - 6) × 18$. It should equal the length obtained from the data for the second man. So $(v - 6) × 18$ = $(v - 8) × 19$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 44km/h.

Let x be the speed of X, then the speed of Y is 6x. So $510/x - 510/{6 × x} = 5.$ Solving, we get x = 85 km/h.