Distance and Time Quiz Set 005

Let the speeds be 11x and 4x. The times they take to cover 100 km are $100/{11x}$ and $100/{4x}$. The ratio would be 4 : 11.

Let the normal speed be x km/hr. We have been given $3/x$ - $3/{x + 4}$ = 1. This translates to the quadratic equation $1x^2 + 4x - 12 = 0$, 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.

We know 1kmph = $5/18$ m/s. So 54kmph = $5/18 × 54$ = 15 m/s.

Let 2x be the actual duration of the journey. Then, $x/6 + x/14 = 40$. Solving for x we get x = 168, and so, 2x = 336 km.

Let the speed of the train be v km/h. Length of the train calculated with the data for the first man = $(v - 3) × 14$. It should equal the length obtained from the data for the second man. So $(v - 3) × 14$ = $(v - 20) × 15$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 258km/h.