On a long stretch of east-west road, A and B are two points such that

350/(x+y) = 1
350/(x-y)=7

350 = x+y
50 = x-y

x=200
y=150
200-150=50

It appears that the information in the question stem that the cars meet after one hour when they are moving towards each other is not really needed to solve the problem.
Let the car starting from A be CA and the car from B be CB and their speeds 'sa' kmph and 'sb' kmph respectively. It is obvious that CB is the faster car since it manages to overtake CA at some point when they both travel eastward.
Let us ignore the first part and focus on the fact that it takes CB seven hours to catch up with CA after they both start simultaneously (CA from point A and CB from point B) moving eastward.
The distance covered by CB in 7 hours is 7*sb kms which is equal to the 350 km plus the the distance covered by CA in 7 hours which is 7*sa kms.
7*sb = 350+7*sa....> (sb-sa) = 50 kmph. ANS: D

Let r = the speed of car 1 and s = the speed of car 2. We can create the following two equations:

r + s = 350

and

7r - 7s = 350

Dividing the second equation by 7, we have r - s = 50. So the difference between their speeds, (r - s), is 50 kmph.

Answer: D

B----------(350km)------------A

Va + Vb = 350 kmph
Let X be the distance A travels in 7 hrs.
Da = X = Va * 7;
Db = 350 + X = Vb * 7;

350 + Va*7 = Vb*7;
350 = (Vb - Va)*7;
Vb - Va = 350/7 = 50;

Correct Ans = D;

ScottTargetTestPrep

Actually you don't need the 1st equation. The 2nd equation is sufficient to solve the problem:
7r-7s = 350....> (r-s) = 350/7 = 50

Given:
1. On a long stretch of east-west road, A and B are two points such that B is 350 km west of A.
2. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour.

Asked: If they both move towards east, then they meet in 7 hrs. What is the difference between their speeds, in km per hour?

B--------------------350 km ---------------------A

Let the speeds of A & B be x & y km/hr respectively

2. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour.
x + y = 350 km/hr (1)

If they both move towards east, then they meet in 7 hrs.
x - y = 350/7 = 50 km/hr (2)

IMO D

On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour. If they both move towards east, then they meet in 7 hrs. What is the difference between their speeds, in km per hour?

A. 20
B. 30
C. 40
D. 50
E. 60


Let A be the speed of A in km
Let B be the speed of B in km

First, look at the question.
We want to know A - B = ??

Second, translate sentences into an equation.
On a long stretch of east-west road, A and B are two points such that B is 350 km west of A. One car starts from A and another from B at the same time. If they move towards each other, then they meet after 1 hour.
This sentence translates into an equation : A + B = 350 -- (1)

If they both move towards east, then they meet in 7 hrs.

This sentence translates into an equation : 7 x A = 350 + 7 x B.
Divide this by 7, we get A = 50 + B -- (2)

Now, since we want to know A - B = ?, (2) alone can answer that.
From (2), we get A - B = 50.
Therefore, the answer is 50.

Can anyone provide a visual representation of this 'long stretch of east-west road' . I can't imagine this