Samir begins riding his bike at a rate of 6 mph. Twelve minutes later, Chris leaves from the same point and bikes along the same route at 9 mph. At any given time, t, the distance traveled can be calculated using the formula d = rt, where d represents distance and r represents rate. How long after Chris begins riding does he catch up to Samir?

Answer:The correct answer option is 24 min.Step-by-step explanation:Let  us assume t to be Chris's time (in hours)  so we can write the following equation:Samir's time (in hours)  [tex]=t + \frac{12}{60} = t + 0.2[/tex]Chris's rate  [tex](r_1)=9 mph[/tex]Samir's rate  [tex](r_2)=6 mph[/tex]Then putting the values in the formula to get:[tex]r_1t = r_2(t + 0.2)[/tex][tex]9t = 6(t + 0.2)[/tex][tex]9t=6(t+0.2)\\\\9t=6t+1.2\\\\9t-6t=1.2\\\\3t=1.2\\\\t=0.4[/tex]t = 0.4 which will be [tex]0.4*60=24[/tex]Therefore, Chris catches up Samir after riding for 24 minutes.