X[A,B,C].............................k.................... .............[M]Y

At X: 3 walkers A, B, C ; speeds a=2, b=8, c=10 respectively.

At Y: motorcyclist M, speed m=14.

Distance XY = k : k is an integer.

All is as in your problem: A,B and C arrive at Y at same time.

The time is minimum, and is an integer.

Also, M's "pickups" are at integer times (you're welcome!)

So find k and the total time.