A wagon train that is one mile long advances one mile at a constant rate. During the same time period, the wagon master rides his horse at a constant rate from the front of the wagon train to the rear, and then back to the front. How far did that wagon master ride?

Question

anonymous · Answer

I need help

anonymous · Answer

x^2 -2r - 1 = 0

anonymous · Answer

Let $v_1$ be the speed of the train and $v_2$ be the speed of the wagon master.

anonymous · Answer

When heading backwards, the master travels $$
v_2+v_1
$$relative the the caravan.

When heading to the front, he travels $$
v_2-v_1
$$relative to the caravan.

anonymous · Answer

The distance traveled relative to the caravan is equal (to one mine) $$
t_1(v_2+v_1)=t_2(v_2-v_1)
$$

anonymous · Answer

The distance the caravan traveled is just: $$
v_1(t_1+t_2)
$$The distance the master travels is $$
v_2(t_1+t_2)
$$