Question 1171389
d=speed*time
200-----x+5-----t-0.5 for E
200------x-------t. for D-L.
xt=200
(x+5)(t-0.5)=200=xt-0.5x+5t-2.5
the two are equal, and xt is common to both and may be removed.
0=-0.5x+5t-2.5
0.5x=5t-2.5, but x=200/t,so 0.5x=100/t
100/t=5t-2.5
100=5t^2-2.5t
0=5t^2-2.5t-100
0=2t^2-t-40
t=(1/4)(1+/- sqrt(1+320); sqrt term=17.92
positive root is (1/4)(18.92)=4.73 hours
slower cyclist had speed of 200/4.73 or 42.28 km/h
faster cyclist had speed to 47.28 km/h, and 200/47.28=4.23 hours

so 47.3 km/h and 42.3 km/h taking 4.2 hours and 4.7 hours.