Question

How do I do this question

Answer 1

The two laws of motion are

$\text{Low:}\ d=v_lt\\\text{Sim:}\ d=v_st$

Since Mr Sim's speed is 15 km/h less that Mr Low's, we have

$\text{Low:}\ d=v_lt\\\text{Sim:}\ d=(v_l-15)t$

Note that the distance d is the same for both equations, because they traveled the same path.

20 minutes is 1/3 of a hour, so at t=1/3 Mr Low traveled the whole distance, while at the same time Mr Sim traveled 4/5 of the distance:

$\text{Low:}\ d=\dfrac{v_l}{3}\\\text{Sim:}\ \dfrac{4d}{5}=\dfrac{(v_l-15)}{3}$

If we multiply Sim's equation by 5/4, we have

$\text{Low:}\ d=\dfrac{v_l}{3}\\\text{Sim:}\ d=\dfrac{5(v_l-15)}{12}$

Since the left hand sides are equal, we equal the right hand side as well:

$\dfrac{v_l}{3}=\dfrac{5(v_l-15)}{12}$

Multiply both sides by 12:

$4v_l=5(v_l-15)$

Expand the right hand side:

$4v_l=5v_l-75 \iff v_l = 75$

Which implies

$v_s=v_l-15=75-15=60$