Questions & Answers

Question

Answers

A. $8:30am$

B. $9:00am$

C. $9:30am$

D. $10:00am$

Answer
Verified

Let the time taken by the bicycle is $t$.

As mentioned in the question the scooter leaves the same town after 1 hour.

Therefore, time taken will be $t - 1$

Now, the distance is the product of speed and time i.e., $d = s \times t$ where s is the speed and t is the time taken.

For bicycle men, speed is $10km/hr$ and time is $t$.

Therefore, the distance traveled by bicycle man will be

$ \Rightarrow d = 10 \times t$

Now, for scooter man, speed is $30km/hr$ and time is $(t - 1)$

Therefore, The distance traveled for scooter man will be

$ \Rightarrow d = 30(t - 1)$

As we know, the distance traveled by bicycle and scooter at the point of overtaking will be the same.

$

\Rightarrow d = 10t = 30(t - 1) \\

\Rightarrow 20t = 30 \\

\Rightarrow t = \dfrac{3}{2}hr \\

$

The time taken by the scooter man is $t - 1 = \dfrac{3}{2} - 1 = \dfrac{1}{2}hr$.

The scooter overtakes the bicycle after half an hour. i.e., $9:30am$