Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M.?

8 kmph

11 kmph

12 kmph

14 kmph

Explanation:

Let the distance travelled by $ x $ km.

Then,$ \dfrac{x}{10} $-$ \dfrac{x}{15} $= 2

$\Rightarrow$ 3$ x $ - 2$ x $ = 60

$\Rightarrow x $ = 60 km.

Time taken to travel 60 km at 10 km/hr =$ \left(\dfrac{60}{10} \right) $hrs= 6 hrs.

So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.

$\therefore$ Required speed =$ \left(\dfrac{60}{5} \right) $kmph.= 12 kmph.