Question

Candice leaves on a long trip driving at a steady rate of 35 miles per hour. Her sister Liz leaves from the same location traveling to the same destination 3 hours later. She drives at a steady rate of 50 miles per hour. How long after Liz leaves home will she catch up to Candice? A. 3 hours B. 10 hours C. 9 hours D. 7 hours

Answer 1

Answer:

D. 7h

Step-by-step explanation:

$v=\dfrac{d}{t}\\\\v-\text{average speed}\\d-\text{distance}\\t-\text{time}\\\\d=vt,\ t=\dfrac{d}{v}\\\\\bold{Candice:}\ v_C=35\ mph,\ d_C,\ t_C\\\\\bold{Liz}:v_L=50\ mph,\ d_L,\ t_L=t-3\\\\\bold{Equation}:\\\\/\text{the distances are the same}/\\\\d_C=d_L\\\\d_C=v_Ct_C,\ d_L=v_Lt_L\\\\35t_C=50(t_C-3)\qquad\text{use the distributive property}\\\\35t_C=50t_C-150\qquad\text{subtract}\ 50t_c\ \text{from both sides}\\\\35t_C-50t_C=50t_C-50t_c-150\\\\-15t_C=-150\qquad\text{divide both sides by (-15)}$

$\dfrac{-15t_C}{-15}=\dfrac{-150}{-15}\\\\t_C=10\\\\t_L=10-3=7$