Question

If a man cycles at $10	ext{ km/hr}$, then he arrives at a certain place at 1 p.m. If he cycles at $15	ext{ km/hr}$, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

Accepted Answer

B. Let distance be $d$ and time taken to reach at 1 p.m. be $t$ hours. $$d = 10t$$ $$d = 15(t - 2)$$ Equating both: $$10t = 15t - 30 \implies 5t = 30 \implies t = 6	ext{ hours}$$ So $d = 60	ext{ km}$. To reach at noon (11 a.m. is $t-2$, 1 p.m. is $t$, so noon is $t-1 = 5$ hours): $$	ext{Required speed} = \frac{60}{5} = 12	ext{ km/hr}$$

Cycling Speed to Arrive at Noon

Explanation

Practise this under exam conditions