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 ?

Fren the answer is D

The shortest way to this kind of problem...

When objects are moving in the same direction...
Step 1
Calculate the difference of speed...
here its...60-50 =10mph

Step 2
initial difference between the two objects...
Since mary is moving at 50 mph...
and paul is 15 minutes behind...
she will be 15/60 x 50 = 12.5 miles away from paul

Step 3...
divide the difference of distance by difference of speed...
i.e. 12.5/10
or 1.25 hr...
1.25 x 60 =75 min or 1 hr 15 min

if the question had asked how long it would take for both to meet from the time mary passed the station then the answer would be
1 hr 15 min + 15 min
=1 hr 30 min
But since the question is asking how long it would take for both to meet from the time paul passed the station the answer will be just 1 hr 15 min...

Answer is D...