A=4t represents the distance (km) Allen travels in time t.
B=5.5t similarly represents the distance Benedict travels.
C=7t represents how far Carl travels.
D=dt+h represents how far Donald travels, where d is Donald’s speed in km/hr and h is the headway Donald has because he leaves before the other cyclists.
When t=10 hr, A=4×10=40km, and D=10d+h.
When t=4 hr, B=4×5.5=22km, and D=4d+h.
Therefore we have:
10d+h=40 because A=D when Allen overtakes Donald.
4d+h=22 because B=D when Benedict overtakes Donald.
Subtracting these two equations we get:
6d=18, so d=3km/hr, Donald’s speed.
And h=22-4d=40-10d=10km, the headway at the start.
So D=3t+10. C=7t, so when C=D, 7t=3t+10, 4t=10, t=2.5hr, the time it takes Carl to overtake Donald.
