Work Distance Problem

Question

It Takes high speed train "x" hours to travel "z" miles distance from A to B. It takes Regular speed train "y" hours to do same distance. If High speed train leaves from A and Regualr speed train leaves from B at same time . how many more miles High speed train would have already travelled than the regualr train when they pass each other??
1) z( y-x)/ x+y
2) z (x-y)/ x+y
3) z (x+y)/ y-x
4) xy (x+y)/ y-x
5) xy (x+y)/ x-y

anordinaryguy · Answer

Now first thing first, Because  y>x  (regular traing will take more time than high-speed train to cover the distance),  so any answer choice contains x-y should be rejected .  That leaves us with A, C, D.

Now you can do the calculation, that will require you 
- to find the average speed of both trains
- to reach to a common point, both will take same time and we need to find out the difference of the distances of that common point from Terminals A and B

on the calculation I find   A   as the right answer

TomB · Answer

can anybody solve the problem by using values for X ,Y , Z. This will help a lot

GMAT011 · Answer

We know the speed of each train is Z/X for the high speed, and Z/Y for the regular (total distance traveled/how much time it used). 
Assume that it took the amount of time "T" for them to pass each other.
Thus distance of high speed train traveled = Z/X*T, and distance of regular speed train traveled = Z/Y*T
Z/X*T+Z/Y*T=Z or (1/X+1/Y)*T*Z=Z
therefore T=XY/(X+Y)

Now we can solve Z/X*T-Z/Y*T, which gives us the answer A.

KarishmaB · Answer

Using ratios can be very helpful too.
To cover the same distance, time taken by high speed:time taken by regular speed = x:y
Therefore, speed of high speed : speed of regular = y:x

Of the total distance, z, distance covered by high speed:distance covered by regular = y:x (in same time)
Distance covered by high speed = z*y/(y+x)
Distance covered by regular = z*x/(y+x)
Difference = z*(y-x)/(y+x)

OR

Put in some values. Say, distance = 10 km
x = 2 hrs
y = 5 hrs
Speed of high speed:speed of regular = 5:2
Of the 10 km, the high speed will cover 10*(5/7)
Regular will cover 10*(2/7)
Difference = 10*3/7

Put in the values of z, x and y in the options to get the answer.

prerit86 · Answer

Thanks! This helps.

Work Distance Problem

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