Problem Solving

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

radhika1306 wrote: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

Answer is E
Mary will cover 12.5 miles in 15 mts and Paul will cover 15 miles in 15 mts (as per the given speeds of both)

In 30 mts Mary will be 25 miles ahead of gas station and Paul will be 15 miles ahead of gas station.

In 45 mts Mary will be 37.5 miles ahead of gas station and Paul will be 30 miles ahead of gas station.

In 1 hr Mary will be 50 miles ahead of gas station and Paul will be 45 miles ahead of gas station.

In 1 hr 15 mts Mary will be 62.5 miles ahead of gas station and Paul will be 60 miles ahead of gas station.

In 1 hr 30 mts Mary will be 75 miles ahead of gas station and Paul will be 75 miles ahead of gas station.

So answer is E

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

jaspreet.sharma is correct, answer is E.

Yop the correct answer is E - I think.

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

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"

.. 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 ..

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

Thanks the Ans is D