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pratikf
09-25-2004, 09:38 PM
Hi,
This is a problem in ETS powerprep:

If two trains r 120 miles apart and are traveling toward each other at a constant rate of 30 mph and 40 mph respectively, how far apart wil they be exactly 1 HOUR BEFORE they meet?

A) 10 miles
B) 30 miles
C) 40 miles
D) 50 miles
E) 70 miles


I am very confused abt speed distance time after seeing this problem. Please help in solving this problem. Thanx.

Econ
09-25-2004, 10:26 PM
(1) Straighforward solution: Let di, ti, ri be the distance, time and rate of train i=1,2. Then the trains will meet/collide in d=t(r1+r2), i.e. in t=12/7 hours. 1 our before that time, i.e. 5/7, train 1 will have covered d1=t1r1=(5/7)30=150/7 and train 2 will have covered 200/7 (in miles). Total is 350/7 i.e. 50 miles. Thus, 1 hour before they meet they will be 120-50=70 miles apart.
(2) Sneaky solution: Notice that 12/7 is less than 2 i.e. the 1 hour that remains for the two trains to collide is more than half of the total time, i.e. the remaining distance is more than half of the total distance. From the answer choices only 70 is greater than 60.

serg14
09-26-2004, 03:57 AM
Seems, your both solutions are too complicated ;)

The speed of approaching trains to each other is 30 mph + 40 mph = 70 mph. The time to meet is 1 hour.
Therefore the decision is 70 mph * 1 h = 70 miles.

pratikf
09-26-2004, 08:06 AM
thanx guys, thanx 4 the help!

neokeynesian
09-29-2004, 08:30 AM
Here is my solution

D=R*T

meeting situation:
h1+h2=D
30h+40h=120
70h=120
h=12/7------->2 trains will be meeting at 12/7 hrs at 0 miles!
How many miles apart will they exactly 1 hr b4 they meet?

12/7h = 120 miles
1 hr = 120/(12/7) =
= (120/12)*7
= 70 miles


hope it helps!

sarahmahmoodkhan
12-12-2007, 06:34 PM
when two trains move towards each other their net speed will be 30+40=70 mph
this means they cover 70 miles in 1 hour

so one hour before they will be 70 miles from each other.SIMPLE!!!!!!!!!

tuanle
12-12-2007, 11:34 PM
70 miles ;)