SOLUTION: A train M leaves station A at 5 a.m. and reaches station B at 9 a.m. Another train N leaves station B at 7 a.m and reaches station A at 10.30 a.m. At what time do the two trains cr

Question 136760: A train M leaves station A at 5 a.m. and reaches station B at 9 a.m. Another train N leaves station B at 7 a.m and reaches station A at 10.30 a.m. At what time do the two trains cross one another?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A train M leaves station A at 5 a.m. and reaches station B at 9 a.m. Another train N leaves station B at 7 a.m and reaches station A at 10.30 a.m. At what time do the two trains cross one another?
:
From the information given, we can say:
:
M takes 4 hrs to go from A to B
and
N takes 3.5 hrs to from B to A
also
Train N leaves B, 2 hrs after M leaves A
:
It will easier if we choose a distance value for A to B
I chose 280 mi, both 4 and 3.5 will divide into it evenly
Find the speed of both trains from this
280/4 = 70 mph speed of M
280/3.5 = 80 mph speed of N
:
When they cross the total distance traveled by both trains = 280 mi
Let t = time (hrs) of train M
then
(t-2) = time of train N
:
Dist = speed * time
70t + 80(t-2) = 280
70t + 180t - 160 = 280
150t = 280 + 160
t =
t = 2 = 2 hrs travel time of M when the cross
:
Change 14/15 hrs to min: 14/15 * 60 = 56 min
:
2 hr 56 min from 5 am = 7:56 am time when they cross.
:
:
Check solution (train N travel time will be 56 min or 14/15 hr
N dist: 14/15 * 80 = 74.67 mi
M dist: 44/15 * 70 =205.33 mi
-------------------------------
Train dist totals: =280 mi
:

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