Question

After what time will he be able to overtake the bus?

• A. $4sec$
• B. $8sec$
• C. $12sec$
• D. $16sec$

Answer 1

Answer: (B)

$8sec$

Let after a time $t$, the cyclist overtake the bus. Then

$96+\frac{1}{2}\times 2\times t{}^2=20\times t$ or $t{}^2-20t+96=0$

$\therefore t=\frac{20\pm \sqrt{400-4\times 96}}{2\times 1}$

$=\frac{20\pm 4}{2}=8sec$ and $12sec$

But since they won't meet again after they have crossed each other once, so only $8$ seconds is the answer since they are headed in different directions.