Two trains leave the depot at the same time, one traveling east and the other traveling west. The speed of one train is 7 mph slower than the other. If after 5 hours the distance between the trains is 175 miles, find the speed of each train.

Question

Two trains leave the depot at the same time, one traveling east and the other traveling west.  The speed of one train is 7 mph slower than the other.  If after 5 hours the distance between the trains is 175 miles, find the speed of each train.

anonymous · Answer

asuming that both have 0 acceleration and constant velocity

anonymous · Answer

$$s_x=v_0 t+s_0$$
$$v=v_0$$

anonymous · Answer

since we're assuming that the station is at (0,0)

anonymous · Answer

so if we're given that velocity of one train is slower than than the other

$$v_{t1}=v_0=v_{t2}-7$$

anonymous · Answer

and $$v_t$$ is just itself

anonymous · Answer

$$s_x=$$ the addition of both displacement equations sooo

$$175=(v-7)t+vt$$

anonymous · Answer

$$175=(v_{t2}-7)(5)+v_{t2}(5)$$


$$175=5v_{t2}-35+5v_{t2}$$
$$210=10v_{t2}$$

$$21mph=v_{t2}$$

since we know 
$$v_{t1}=v_{t2}-7$$
$$v_{t1}=21-7=14mph$$

anonymous · Answer

lastly check to make sure

anonymous · Answer

the distance of train 1 would be

$$s_{t1_{x}}=v_{t1}t=14(5)=70miles$$

anonymous · Answer

$$s_{t2_{x}}=v_{t2}t=21(5)=105miles$$

105+70 = 175

anonymous · Answer

answers are

one train at 14 mph and the other at 21 mph