Two trains T1 and T2 arrive at Station S at 1:00 P.M. After a halt of

Question

Two trains T1 and T2 arrive at Station S at 1:00 P.M. After a halt of half an hour, train T1 left the station at 1:30 P.M. and travelled at a constant speed of 30 miles per hour in a straight line towards north from Station S. Train T2 departed from Station S at 2:00 P.M. and travelled at a constant speed of 100 miles per hour in a straight line towards south from the Station S. If both the train travelled indefinitely without changing their initial directions, what is the ratio of time it takes T2 to cover 1/3rd of the distance that T1 has travelled to the time it takes T2 to cover thrice the distance that T1 has travelled?
A. 1:81
B. 1:18
C. 1:4
D. 4:1
E. 81:1

figjam786 · Answer

SaquibHGMATWhiz 
 ThatDudeKnows

Can any of you, please provide explanation to this question?

av1901 · Answer

Let time travelled by T2 be x hours
So time travelled by T1 is (x+0.5) because T1 starts half hour earlier

We will form 2 equations, one for 1/3 distance travelled and 1 for thrice distance travelled

Eq 1: (1/3 distance)

100 * x = 1/3 * 30 * (x+0.5)

What we are saying here is the left hand side is the distance travelled by T2 and the right hand side is 1/3 of the distance travelled by T1

Solving for x = 1/18 hours

Eq 2: (3 x Distance)

100 * x = 3 * 30 * (x+0.5)

What we are saying here is the left hand side is the distance travelled by T2 and the right hand side is 3 times of the distance travelled by T1

Solving for x = 4.5 hours

Ratio = (1/18) / 4.5 = 1/81

Answer - A

Posted from my mobile device

ThatDudeKnows · Answer

figjam786

First, I'll point out that there is a wording error in the question. We are asked for the ratio of two times but are not told whether to start timing when T1 leaves the station or when T2 leaves the station. I'll assume the later.

Two ways.

First, the algebra.
T2 travels at 100mph so travels 100T miles in T hours.
T1 travels at 30mph so travels 30T miles in T hours. T1 left 30 minutes before T2, so we need to add 15 miles to T1's distance.
We need to find the ratio between T when 100T=1/3(30T+15) : 100T=3(30T+15)

100T = 1/3(30T+15)
100T = 10T+5
90T = 5
T = 1/18

100T = 3(30T+15)
100T = 90T+45
10T = 4.5

1/18 : 4.5
1:81
Answer choice A.

Second, what if you have no idea where to start on the algebra? Just start trying to figure stuff out.
At 2:00, T1 has gone 15 miles and T2 has gone 0 miles.
At 3:00, T1 has gone 45 miles and T2 has gone 100 miles.
At 4:00, T1 has gone 75 miles and T2 has gone 200 miles.
At 5:00, T1 has gone 105 miles and T2 has gone 300 miles. Ooooh, that's getting close to T2 being 3x T1.
At 6:00, T1 has gone 135 miles and T2 has gone 400 miles. Even closer. T2 needed to go 5 more miles.
At 7:00, T1 has gone 165 miles and T2 has gone 500 miles. Wait a second, that's too long. 500 is 5 miles more than 3*165.
At 6:30, T1 has gone 150 miles and T2 has gone 450 miles. Okay, that's 3x!
What about 1/3x? Well, at 3:00 we had already passed that. How about 2:30?
At 2:30, T1 has gone 30 miles and T2 has gone 50 miles. Need an earlier time.
At 2:15, T1 has gone 22.5 miles and T2 has gone 25 miles. Still need earlier.
At 2:06, T1 has gone 18 miles and T2 has gone 16.7 miles. Still need earlier!
Oh, boy, our ratio is going to be REALLY small. 
Answer choice A.

figjam786 · Answer

ThatDudeKnows 
 I thought wordings were clear (Refer Bold statements below).
Please let me know if my understanding is flawed here.

Two trains T1 and T2  arrive at Station S at 1:00 P.M . After a halt of half an hour, train  T1 left the station at 1:30 P.M . and travelled at a constant speed of 30 miles per hour in a straight line towards north from Station S.  Train T2 departed from Station S at 2:00 P.M.  and travelled at a constant speed of 100 miles per hour in a straight line towards south from the Station S. If both the train travelled indefinitely without changing their initial directions, what is the ratio of time it takes T2 to cover 1/3rd of the distance that T1 has travelled to the time it takes T2 to cover thrice the distance that T1 has travelled?
A. 1:81
B. 1:18
C. 1:4
D. 4:1
E. 81:1

ThatDudeKnows · Answer

Note that this is not important, since I don't think GMAC would leave an ambiguity of this type. If you can solve it either way, you're all good!!

The ratio of the time from 1:30 until T2 has covered 0.333x/3x of T1?
Or the ratio of the time from 2:00 until T2 has covered 0.333x/3x of T1?

If you give someone a head start in the race, does the race start when  they  cross the starting line or when  you  cross the starting line? 
This question works if use the second option, but not if we use the first.

bumpbot · Answer

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Two trains T1 and T2 arrive at Station S at 1:00 P.M. After a halt of

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Two trains T1 and T2 arrive at Station S at 1:00 P.M. After a halt of

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