Two trains started simultaneously from opposite ends of a

Train X : 100 m in 5 hrs
speed = 100/5 = 20mph
Train Y : 100 m in 3 hrs
speed = 100/3 mph

The distance shrinking at effective speed (20 + 100/3 ) mph
Time of intersect = 100 / (20+100/3) = 15/8 hrs
Distance travelled by X < Distance travelled by Y

Distance travelled by X = time * speed = 15/8 * 20 = 75/2

Bunuel, could you please explain this. It is not clear to me. thanks!

Since, the ratio of times of X and Y to cover the same distance of 100 miles is is 5:3, then the ratio of their rates is 3:5. Consider this, say the rates of trains X and Y are X and Y respectively, then:

Distance=Rate*Time --> X*5=Y*3 --> ratio of the rates is X:Y=3:5. At the time they meet, so after they travel the same time interval the ratio of distances covered by X and Y would also be in that ratio (for example if X=3 mph and Y=5 mph then they would meet in 100/(3+5)=100/8 hours, hence train X would cover 300/8 miles and train Y would cover 500/8 miles --> ratio of distances covered (300/8):(500/8)=3:5).

Now, since the the ratio of distances covered by X and Y is 3:5 then X covered 3/(3+5)=3/8 of the total distance.

Hope it's clear.

Why is that when the meet they would have covered 100 miles? This bit is little confusing.

When they meet one train covers some part of 100-mile distance and another covers the remaining part of 100-mile distance, so combined they cover 100 miles.

Speed of first train: 100/5 = 20 Mph
Speed of second train: 100/3 = 33.33 Mph

Now in 1 hr distance covered by X is 20 & that by Y is 33.33.In the next hr it will be 40 & 66.66 resp.
40+66.66=106.6> the distance between them...So they would have met by now & the answer would be something less than 40..which leaves us with A

The combined distance traveled by the two trains was 100 miles. Each train traveled for t hours. We can create the distance equation:

100/5 * t + 100/3 * t = 100

Multiplying by 15 to clear the fractions from the equation, we have:

300t + 500t = 1500

800t = 1500

t = 15/8

Thus, train X had traveled 15/8 x 100/5 = 15/8 x 20 = 37.5 miles by the time it reached Y.

Answer: A

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Karishma explaining a similar question to this.

The time travelled by both the trains X & Y is equal when they meet.

If Train X travelled distance D, train Y travelled 100-D

Time travelled by Train X = D / 20. Time travelled by Y = (100- D)/(100/3) = 3(100-D)/100

Now D / 20 = 3 (100-D)/100
5D = 300 - 3 D, 8D = 300
So the distrance travelled X i.e. D = 300/8 = 37.5 answer A

If both X and Y have same speed, they will meet in the middle. In this case, both X and Y will travel 50 miles
Now X is slower than Y, so X will travel less than 50 miles whereas Y will travel more than 50.
So we can reject C,D,E before starting the calculation because the answer must be less than 50

Now A & B are left
Let's pick B because 40 seems a nice number (no decimals)
Speed of X = 100/5=20, Speed of Y= 100/3=33.3
Now if X has travelled 40 miles, time taken is 40/20 = 2 hrs
Y has travelled 33.3*3=66 miles
So the distance doesn't add up to 100 (40+66 = 106)
Therefore A is correct

Train X completed the 100-mile trip in 5 hours
Speed = distance/time = 100/5 = 20 mph

Train Y completed the 100-mile trip in 3 hours
Speed = distance/time = 100/3 ≈ 33 mph (This approximation is close enough. You'll see why shortly)

How many miles had Train X traveled when it met Train Y?
Let's start with a word equation.
When the two trains meet, each train will have been traveling for the same amount of time
So, we can write: Train X's travel time = Train Y's travel time

time = distance/speed
We know each train's speed, but not the distance traveled (when they meet). So, let's assign some variables.

Let d = the distance train X travels
So, 100-d = the distance train Y travels (since their COMBINED travel distance must add to 100 miles)

We can now turn our word equation into an algebraic equation.
We get: d/20 = (100 - d)/33
Cross multiply to get: (33)(d) = (20)(100 - d)
Expand: 33d = 2000 - 20d
Add 20d to both sides: 53d = 2000
So, d = 2000/53

IMPORTANT: Before you start performing any long division, first notice that 2000/50 = 40
Since the denominator (53) is greater than 50, we can conclude that 2000/53 is LESS THAN 40
Since only one answer choice is less than 40, the correct answer must be A

Lets find out the Speed first of both the trains.
X - 100/5 = 20 Miles/Hour
Y - 100/3 = 33.33 Miles/Hour

Now , lets visualize the problem

0----------------------------------------------0
X starts from here

0-----------------------------------------------0 Y Starts from here


Now after 1 hour lets understand the position of both the trains.
See Image

After 2 hours the position will be

See Image

After 2 hours of travelling both the trains must have crossed each other.
If the distance travelled by Y after 2 hours would have been 60 Miles. Then they both have met exactly after 2 hours and X would have travelled 40 Miles.

But Since Y travelled for 66.66 Miles , then it is sure that X and Y must have met before X travelled 40 Miles.

Hence Answer is A.

Thanks.

Since the train X is travelling at a speed of 100 miles per 5 hours,
Speed per hour = 100/5 = 20 miles per hour

Similarly, the speed of the train Y = 100/3 miles per hour.

Since the distance between the trains is 100 miles, and the trains are travelling toward each other,

Time to meet = 100/(20+100/3) = 300/160 = 15/8 hours.

Distance covered by X to meet Y = 15*20/8 miles = 37.5 miles.

Thus, the correct option is A.

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