If two people are running at 18 km/h and 21.6km/h, and the one who is running 21.6hm/h starts 200 meters behind the starting line, then when do they meet, and at what distance did each one run? Also, how do you solve this without a calculator?
Answers (1)
If we write a(t) for the position of first runner (the one running at 18km/h) at time t (in hours) and b(t) for the position of the second runner at time t (in hours). Choosing the origin to be at the position of the first runner at time 0 we have:
a(t)=0 + 18t
b(t)=-0.2 +21.6t (since 200m=0.2km)
To answer the first question we should solve for t in the equation
a(t)=b(t)
18t= -0.2+21.6t
0.2=(21.6-18)t=3.6t
t=0.2/3.6=2/36=1/18
Distance first runner ran = a(1/18)-a(0)=18(1/18)=1km
Distance second runner ran = Distance first runner ran + 0.2 = 1.2km.