A pedestrian and a cyclist start simultaneously towards each other from New York and Las Vegas which are 40 km apart and meet 2 hours after the start. Then they resumed their trips and the cyclist arrives at New york 7 hours 30 minutes earlier than the pedestrian arrives at Las Vegas. Which of these
could be the speed of the pedestrian?
My Try: suppose they meet at certain point x km from New York pedestrain speed will be x/2 km/hr(D=S*T),
for cyclist speed will be (40-x)/2 km/hr.
so time taken by cyclist to cover the 40 km will be: 80/(40-x) hr and time taken by pedestrian will be 80/x.
So according to question they say that cyclist reach 7 hr 30 min earlier so what i think is
(80/(40-x) + 15/2)hr = 80/x hr
This is my Understanding of the question am i going on right way ?
Best Answer
Basically, we want to solve thos syatem of two equations in unkonws $v_C$ and $v_P$: $$\left\{\begin{matrix} \frac{40-2v_C}{v_C}-\frac{40-2v_P}{v_P}=7.5 \\ 2v_P+2v_C=40 \end{matrix}\right.$$ This can be solved substituing $v_P=\frac{40-2v_C}{2}$ and we obtain the same as your solutions. In particular, we have: $$7.5v_C^2-230v_C+800=0\leftrightarrow v_C=4 \vee v_C=\frac{80}{3}$$ Substituing, we have: $$v_P=16 \;\;\;\text{IMPOSSIBLE} \vee v_P=-\frac{20}{3}$$