set 24 q 36

radhika1306 · Posted: Tue Sep 04, 2007 3:00 pm Post subject: set 24 q 36

Mary passed a certain gas station on a highway while traveling west at a constant
speed of 50 miles per hour. Then, 15 minutes later, Paul passed the same gas station
while traveling west at a constant speed of 60 miles per hour. If both drivers
maintained their speeds and both remained on the highway for at least 2 hours, how
long after he passed the gas station did Paul catch up with Mary?
A. 30 min
B. 45 min
C. 1 hr
D. 1 hr 15 min
E. 1 hr 30 min

jaspreet.sharma · Posted: Tue Sep 04, 2007 3:38 pm Post subject: Re: set 24 q 36

blah45 · Posted: Tue Sep 04, 2007 5:09 pm Post subject:

is it (C)?

D = RT

T = D/R = (50 * 1/4) / 10 = 1.25 hrs total time

Time it took after passing the gas station 1.25 hr - 15mins = 1hr

agps · Posted: Wed Sep 05, 2007 2:55 am Post subject:

jaspreet.sharma is correct, answer is E.

Guest · Posted: Wed Sep 05, 2007 5:02 am Post subject: Equation

I agree that the correct answer is E, but can anyone show me the correct algebraic equation to set up here in order to arrive at 1.5 hours? I'm getting 1.25 hours using equations.

camitava · Posted: Wed Sep 05, 2007 5:14 am Post subject:

Yop the correct answer is E - I think.

agps · Posted: Wed Sep 05, 2007 5:44 am Post subject:

jaspreet posted a good explanation, what don't you understand about it?

samirpandeyit62 · Posted: Wed Sep 05, 2007 6:48 am Post subject:

According to me the ans should be "D" 1 hr 15 mins

As per Jaspreet's explanation, Pual took 1 hr 30 mins i.e 90 mins to
catch up with Mary

Now his speed is 60 miles/hr i.e 1mile/minute

hence to travel 75 miles he will take 1 hr 15 mins only i.e 75 mins
& not 90 mins i.e. 1 hr 30 mins

The problem can solved as such

let t be time taken by Paul to catch up with Mary
Mary's time would be t+1/4 hrs (15 mins more than Paul)

Distance covered by both would be same say d

hence for Paul we can say 60Xt =d
for Mary we can say 50(t+1/4) = d

hence 60t = 50(t+1/4)

hence t = 1.25 hrs =1 hr 15 mins

So the ans should be "D"

gabriel · Posted: Wed Sep 05, 2007 9:54 am Post subject:

.. a simple problem based on relative speed ..

Forget everything that happens before the gas station .. consider the gas station to be the starting point ..

.. from the starting point Mary travels for 15 min at 50 miles/hr .. so in 15 minutes Mary traveled a distance of 12.5 kms.. when Mary has traveled for 15 min Paul starts from the starting point ( the gas station) .. the distance between both of them is 12.5 kilometers ..

.. now comes the concept of relative speed .. since they both are travelling in the same direction the time taken for Paul to catch up with Mary is 12.5/(60-50) hrs = 1.25 hrs = 1 hr and 15 minutes ... ans is D ..

agps · Posted: Wed Sep 05, 2007 3:43 pm Post subject:

my mistake was to consider the 15 min before Paul left the gas station, those don't count. Laughing

radhika1306 · Posted: Thu Sep 06, 2007 6:43 am Post subject:

Thanks the Ans is D