Time and Distance problem

The answer is 10hours and 9hours. I will post a detailed explanation in a bit. Before that, Can you please cite the source of the question please? It doesn't look like a GMAT type question.

guerrero wrote:Hello All,

I am not able to figure out a solution for this -please help me solve this with explanation


Two trains A & B start frm stations X & y towards each other.B leaves station Y half an
hour aftr train A leaves station X.two hrs aftr train A has strtd,the dist between the
trains A & B is 19/30th of the dist between stations X & y.how much time would it take
each train (A & B) to cover the distance X to Y,if train A reaches half an hr later to its
destination as compared to B.

ans-
a)8hrs,6hrs
b)10hrs,9hrs
c)5hrs,4hrs
d)9hrs,8hrs

thanks!

We can plug in the answers, which represent A's time and B's time.
Since A leaves 1/2 hour earlier and finishes 1/2 later than B, A's time must be 1 hour longer than B's time.
Eliminate A.

Answer choice B: A = 10 hours, B = 9 hours
Let the distance = 90 miles.
A's rate = d/t = 90/10 = 9 miles per hour.
B's rate = d/t = 90/9 = 10 miles per hour.
Distance traveled by A in 2 hours = r*t = 9*2 = 18 miles.
B leaves 1/2 hour later.
Distance traveled by B in 1.5 hours = r*t = 10(1.5) = 15 miles.
Total distance traveled by A and B = 18+15 = 33 miles.
(Remaining distance between A and B)/(total distance) = (90-33)/90 = (30-11)/30 = 19/30.
Success!

The correct answer is B.

Mitch Thank you so much for a very clear approach . wish i could tackle the Math like you

GMATGuruNY wrote:

guerrero wrote:Hello All,

I am not able to figure out a solution for this -please help me solve this with explanation


Two trains A & B start frm stations X & y towards each other.B leaves station Y half an
hour aftr train A leaves station X.two hrs aftr train A has strtd,the dist between the
trains A & B is 19/30th of the dist between stations X & y.how much time would it take
each train (A & B) to cover the distance X to Y,if train A reaches half an hr later to its
destination as compared to B.

ans-
a)8hrs,6hrs
b)10hrs,9hrs
c)5hrs,4hrs
d)9hrs,8hrs

thanks!

We can plug in the answers, which represent A's time and B's time.
Since A leaves 1/2 hour earlier and finishes 1/2 later than B, A's time must be 1 hour longer than B's time.
Eliminate A.

Answer choice B: A = 10 hours, B = 9 hours
Let the distance = 90 miles.
A's rate = d/t = 90/10 = 9 miles per hour.
B's rate = d/t = 90/9 = 10 miles per hour.
Distance traveled by A in 2 hours = r*t = 9*2 = 18 miles.
B leaves 1/2 hour later.
Distance traveled by B in 1.5 hours = r*t = 10(1.5) = 15 miles.
Total distance traveled by A and B = 18+15 = 33 miles.
(Remaining distance between A and B)/(total distance) = (90-33)/90 = (30-11)/30 = 19/30.
Success!

The correct answer is B.