
question 1. Initial distance is 240.
let the equilateral triangle's side be d. so d/a=d120/b
also as a reaches first so a>b hence right angle is formed in A's path thus after B travels 80 miles, A has traveled d((d80)cos60) i.e. hence second equation is 80/b=(d/2 + 40)/a.
equate a/b from both solve the quadratic in d.
question 2. this is quite straight forward. while going kate very astutely walks for twice the time as she runs (like everyone of us ;)) so eq. 1 is 80v/3=d where v is the walking speed and d is the dist. between her home and school. second eq. is 5x=d/v where x is the time she walks whilst coming back from school. hence x=16/3.
