Train X and train Y pass one another traveling in opposite directions.

Question

Train X and train Y pass one another traveling in opposite directions. Forty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?

A. 28
B. 40
C. 60
D. 72
E. 80

Kudos for a correct solution.

A. 28
B. 40
C. 60
D. 72
E. 80

Kudos for a correct  solution .

robertsonsd · Accepted Answer

The easiest way to think about this problem is to start off conceptually.

If the total distance between the trains after 2/3 hours (40 minutes) is 100 miles, then the  combined  speed of the trains must be 150 mph. (using RTD tables, 100 * 3/2 = 150)
Therefore, if train x is going 30 mph faster than train y, then train x's speed must be -> x + (x-30) = 150 -> x = 90

Therefore, after 40 minutes, traveling at 90 mph, train x has traveled  60 miles  (90 * 2/3 hours = 60 miles).

AVRonaldo · Answer

Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30)   i.e. 2R+30

d=100 and t = 40 min i.e 40/60 hr

using RTD table, (2R+30) * 40/60 = 100 ==> R= 60 miles/hr

So the rate of train X is 90 miles/hr (since R+30)

The distance traveled by Train X in 40 min is R*T = 90 * 40?/60 = 60 miles (C)

shreyast · Answer

Let's say train X runs at z miles/hour, then train Y will be running at (z-30) miles/hour
Since they are 100 miles apart after 40 minutes = 40/60 hours = 2/3 hours

z*\frac{2}{3} + (z-30)*\frac{2}{3} = 100 
 2*z*\frac{2}{3} -20 = 100 
 z*\frac{2}{3} = 60  = distance travelled by train X in 40 minutes.

Lucky2783 · Answer

x=Speed of Train X
y= X-30 
relative speed = 2X-30 
T= 2/3 hr

(2X-30) *2/3= 100 
X=90 mph

distance travelled = 90*2/3 = 60

Answer C

jugglerG2 · Answer

Its a relative speed problem.

Relative speed of train X with reference to train Y = 100*60/40 = 150

Since train X and Y are going in opposite direction, the relative speed would be sum of individual speeds.
Hence,

x -30 + x = 150 => x=90.

Speed of train X is 90 and hence distance traveled in 40 minutes would be 90*40/60 = 60 miles.

C is the correct answer.

architbansal · Answer

Answer is "C"

if they travel 100 miles in 40 mins 
=> in 1 hr they will travel (100/40)*60 = 150 miles
assume speed of train X = y+30
and seepd of 2nd train = y
now since the trains are moving in different directions the speed of both the trains add up
=> y + 30 + y = 150 (because in one 1 hr they travel 150 miles)
=> 2y + 30 = 150 
=> y = 60 
=> speed of train x = 90 
hence in 40 mins it will travel 60 miles ( 90 *40/60)

brs1cob · Answer

let's say speed of y be a km/h and speed of x is (a+30)km/h
since they are traveling in opposite directions, we need to add their speed,
therefore total speed is a+a+30 =(2a+30)km/h
in 2/3 = 0.66 hours they traveled 100 km, so distance/time = speed
100/0.66=2a+30
a=60km/h
so speed of x is 60+30 = 90km/h
and x will cover 90*(2/3) = 60km

Temurkhon · Answer

(2/3)x + (2/3)*(x+30)=100

(4/3)*x=80

x=60

60+30=90*(2/3)=60

C

Mahmud6 · Answer

For relative speed of bodies moving in opposite direction, the equation is (Sx + Sy) X t = Distance

Here, total distance need to be covered is 100 miles

Let the speed of train Y is y. Therefore, the speed of train X would be y+30.

So, the equation becomes  (y+3+y)t=100=>y=60

So, the speed of train X is 60+30=90

In 60 minutes train x travels 90 miles. So in 40 minutes it will travel 60 miles.

Archit3110 · Answer

from given info
speed of train X; x
speed of train Y ; y
given ; speed of train X ; y+30
so ;
(2y+30)*40/60 = 100
y = 60 mph
x= 90mph
distance of X will be 90*40/60 ; 60 miles 
IMO C

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Train X and train Y pass one another traveling in opposite directions.

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