A starts from X at 9:00 am and reaches Y at 1:00 pm. B starts from Y

Question

A starts from X at 9:00 am and reaches Y at 1:00 pm. B starts from Y at 10:00 am and reaches X at 4 pm. At what time do the two meet?

A. 11:42 am.
B. 11:46 am.
C. 11:48 am.
D. 11:50 am.
E. 11:52 am.

PTD1995 · Accepted Answer

Option C 
A takes 4 hours to travel XY and B takes 6 hours to travel XY. Thus, A will travel  \frac{1}{4}  each hour, and B will travel  \frac{1}{6}  respectively.

Since A starts 1 hour earlier than B starts, by 10 am he would have covered  \frac{1}{4}  of the way. 
So, A and B are separated by  \frac{3}{4}  of the way.

Thus,
 \frac{1}{4}h+\frac{1}{6}h=\frac{3}{4} 
Yielding,
 h=\frac{9}{5} , corresponding to 1h and 48min.
Since we started this at 10AM:  10+1:48=11:48

BrentGMATPrepNow · Answer

APPROACH #1 : Use shrinking gap properties
Let d = the distance between X and Y

A can travel the entire distance in 4 hours, which means A's RATE = distance/time = d/4
B can travel the entire distance in 6 hours, which means B's RATE = distance/time = d/6
So, the rate at which the gap between A and B shrinks = d/4 + d/6 = 3d/12 + 2d/12 =   5d/12

At 9am, the distance between A and B is d. 
Over the next hour, the distance person A travels  = (rate)(time) = (d/4)(1) = d/4 
So, at 10am, the distance between A and B  = d - d/4 = 3d/4

Time for gap to shrink to zero = distance/(shrink rate) = ( 3d/4 )/(  5d/12  ) = (3d/4)(12/5d) = 36d/20d = 36/20 = 9/5 = 1 4/5 hours =  1 hour and 48 minutes

So the time at which they met = 10:00 am + 1 hour and 48 minutes = 11:48 am

Answer: C

APPROACH #2 : Start with the word equation
Let d = the distance between X and Y

A can travel the entire distance in 4 hours, which means A's RATE = distance/time =  d/4 
B can travel the entire distance in 6 hours, which means B's RATE = distance/time =  d/6

Since A starts traveling 1 hour before B starts traveling, we know that B's travel time is  1 hour less than A's travel time 
So, if we let  t  = A's travel time, it must be the case that  t - 1  = B's travel time.

When A and B meet, the SUM of their distances traveled must be d. 
So, we can write the following word equation:  ( A's distance traveled ) + ( B's distance traveled ) = d

Distance = (rate)(time) , which means we can substitute values to get:   (d/4)(t)  +  (d/6)(t - 1)  = d 
Eliminate the fractions by multiplying both sides of the equation by 12 to get:  (3d)(t) + (2d)(t - 1) = 12d 
Divide both sides of the equation by d to get:  3t + 2(t - 1) = 12 
Expand and simplify the left side:  5t - 2 = 12 
Solve:  t = 14/5 = 2 4/5 hours = 2 hours and 48 minutes

Since t = A's travel time, we know that the two travelers meet 2 hours and 48 minutes after A started traveling.
9:00 am + 2 hours and 48 minutes = 11:48 am

Answer: C

youcouldsailaway · Answer

I found it easier to use some value for distance to arrive at the answer. My approach is as follows:

To get an integer for speed, let's use 24 miles for distance.

Speed of A = 24 / 4 = 6 mph
Speed of B = 24 / 6 = 4 mph

They both are working towards a common goal, so we add their speeds. Thus, combined speed = 6 + 4 = 10 mph.

Now, before moving to the next step, i.e, finding time using the formula, we need to remember that A & B started their journeys at different times. Thus, A has already has covered some distance which doesn't need to be covered by either of them in order to meet each other. So we will subtract this distance.

Since A started his journey before B, he has already covered 6 miles (given his speed of 6 mph) and thus, the remaining distance is 18 miles.

Time = 18 miles / 10 mph 
Time = 1.8 hrs 
Time = 1.8 * 60 = 1 hr 48 mins.

We will add this to A's time since he is the one who started the journey and so he is the point of inception / beginning point.

Thus, answer is C.

bumpbot · Answer

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A starts from X at 9:00 am and reaches Y at 1:00 pm. B starts from Y

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