On a Monday, John left from his home for his office at 09:05 AM and reached his office at 10:00 AM. On Tuesday, he left from his home for his office 15 minutes later than the time he left his home on Monday and reached his office 4 minutes later than the time he reached his office on Monday. If on Tuesday, John drove at an average speed that was 15 kilometres per hour faster than his average speed on Monday, how far in kilometres was his office from his home?
A. 50
B. 55
C. 60
D. 65
E. 75
Hi all!
Let me guide you using the approach of proportions(Caution- Its a Good to know approach not Must to know for GMAT
Treat it like an
add on to your knowledge basket
) .
GMAT Track of thought 1On Monday, John utilised 55min to travel from his home to office.
On Tuesday he started off at 9:20am and reached the office at 10:04 am according to the question which implies he utilised 44min to travel from home to office.
What is the drop in the time? Its 55-44 or 11 min.
As a fraction or ratio with respect to the initial time, the decrease in time is change in time/initial time = 11/55 =1/5
Technique / Approach used: For any two variables that are inversely related, like speed and time (distance is constant) ,price and consumption (when expenditure is constant) imagine a straight line
One end of the line say the right side mention any increase/profit/all more or+ values and on the other mention the corresponding decrease/loss/less or - values.
(Like in this case, Time has decreased and this is because speed has increased with distance remaining constant)
Whenever there is a decrease in one of the variables by a factor of x/y , the corresponding increase in the other variable is x/(y-x).
Whenever there is an increase in one of the variables by a factor of x/y, the corresponding decrease in the other variable is x/ (y +x)Say if the speed increased by 25% = 1/4 x=1,y=4 ,the decrease in time is 1/(1+4)= 1/5 =20%
Coming back to the question
GMAT Track of thought 2If the decrease in time is by a factor of 1/5(x=1,y=5), the increase in speed that has caused this must have been = x/(y-x) = 1/(5-1)= 1/4
This fractional value is equivalent to 15
=> 1/4 = 15
=>1 or initial speed = 15 * 4 = 60km
Keeping an eye on the question-
GMAT Track of thought 3How far in kilometres was his office from his home? I need to compute the Distance between his home and office.
Distance = Initial Speed * Initial Time = 60 * 55min = 60 * 55/60 hr = 55 km
Option B
However, I don't remember using this technique in official questions!
Again,its a good to know approach, NOT must to know according to me!Setting up equations can be an alternate approach already mentioned by a
divyadna here.
Hope you all are learning well
Let me know if you have any questions!
Devmitra Sen
GMAT Mentor