Question

Two bikes get closer by $10\text{m}$ every second while travelling in the opposite directions. They get closer by $1\text{m}$ in every second while travelling in the same directions. The speeds of the two bikes will be:

• A. $5\text{m/s},5.5\text{m/s}$
• B. $5.5\text{m/s},4.5\text{m/s}$
• C. $4.5\text{m/s},4\text{m/s}$
• D. $5\text{m/s},5\text{m/s}$

Answer 1

The correct option is B $5.5\text{m/s},4.5\text{m/s}$

When moving in opposite direction the two bikes get closer by $10\text{m}$ every second
Distance covered per second is speed
So, we can say that their relative speed when moving in opposite direction is $10\text{m/s}$
When moving in opposite direction

$v_1+v_2=10\text{m/s}$ …(i)
When moving in same direction

$v_1–v_2=1\text{m/s}$ …(ii)
Adding (i) and (ii)
$2v_1=11$
$v_1=5.5\text{m/s}$
Subtracting (ii) from (i)
$2v_2=9\text{m/s}$
$v_2=4.5\text{m/s}$
Therefore option b is the correct answer.