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

Ans e

Can you please suggest the shortest way to this ?

nehakhas1 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

Ans e

Can you please suggest the shortest way to this ?

I dunno why but I am getting D as my answer.

R of mary = 50
T = t + 1/4 since mary was already 15 minutes on the road when Paul passed the gas station.

R of paul = 60
T = t

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

50t + 50/4 = 60t

t = 1.25

convert that into minutes = 75 minutes which is 1 hr and 15 minutes.

Yes u r write,
P will catch M = 75 min
But M time = 90 min.

Any way shortest way is:
Difference in Speed=10
Distance (When P started)=12.5
So Time=12.5/10=1.25 hrs = 75 min.

Vikas Panwar

ssmiles08 wrote:

nehakhas1 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

Ans e

Can you please suggest the shortest way to this ?

I dunno why but I am getting D as my answer.

R of mary = 50
T = t + 1/4 since mary was already 15 minutes on the road when Paul passed the gas station.

R of paul = 60
T = t

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

50t + 50/4 = 60t

t = 1.25

convert that into minutes = 75 minutes which is 1 hr and 15 minutes.

1:15 is incorrect.

The question is how long it would take for you to catch up with Mary after you pass the gas station. Since it took 15 minutes to catch up at 60mph, that means he has traveled 15 miles.

Mary x time + 15 miles = Paul x time

50t+15 = 60t
which equals
15 = 10t
t=3/2 hours or 1.5 hours.

hwiya320 wrote:1:15 is incorrect.

The question is how long it would take for you to catch up with Mary after you pass the gas station. Since it took 15 minutes to catch up at 60mph, that means he has traveled 15 miles.

Mary x time + 15 miles = Paul x time

50t+15 = 60t
which equals
15 = 10t
t=3/2 hours or 1.5 hours.

Mary traveled the 15 minutes at 50 mph before paul reached the gas station. So she traveled 12.5 miles. (you used 60 mph instead of 50 for the distance mary traveled before paul reached the gas station).

Therefore it is

50t + 12.5 = 60t
12.5 = 10t
t = 1.25