Question

In a journey of total 24 km, a man noticed that after cycling for 1 hour 40 minutes, the distance covered by him was \( \frac{5}{7} \) of the remaining distance. What was his speed in meters per second?

• A. \( 1 \frac{1}{3} \)
• B. \( 1 \frac{2}{3} \)
• C. \( 1 \frac{5}{6} \)
• D. \( 1 \frac{1}{4} \)

Hint:

Always convert time into hours or seconds and distance into consistent units before applying the speed formula.

Answer 1

The Correct Option is B

Let distance covered = \( x \) km Remaining = \( 24 - x \) km Given: \[ x = \frac{5}{7}(24 - x) \Rightarrow 7x = 5(24 - x) \Rightarrow 7x = 120 - 5x \Rightarrow 12x = 120 \Rightarrow x = 10 \text{ km} \] Time = 1 hr 40 min = \( \frac{5}{3} \) hours Speed = \( \frac{10}{5/3} = 6 \) km/h = \( \frac{6000}{3600} = \frac{5}{3} \) m/s = \( 1 \frac{2}{3} \) m/s