Mary goes from her house to the library at a constant speed rate of 40 miles per hour and come back from the library to her house at a constant rate of 45 miles per hour along the same route. What is the distance of the route?
(1) The difference between the round trip’s times taken is 2 minutes
(2) The total amount of minutes for the round trip taken is 34 minutes
Soln: Lets the distance from Home to library be d
Speed * time= distance Hence 40*t1=d
Similarly for library to home 45*t2=d
as distance is same we can equate both i.e 40*t1=45*t2
(Rem- speed is given to us in miles/hour, where as if we see in both statements time is given in mins)
so its better to convert into mins
40/60*t1=45/60*t2
simplifying ,2/3t1=3/4t2
Now lets check each statement
(1) The difference between the round trip’s times taken is 2 minutes
t1-t2=2mins
hence t1= t2+2
we can replace this in equation 2/3t1=3/4t2 and get the time and hence the distance.
So st 1 is sufficient
St 2 The total amount of minutes for the round trip taken is 34 minutes
Here we are given t1+t2=34
t1=34-t2
Again can replace this in equation 2/3t@1=3/4t2 and get t1 and t2 and also cal distance/
St 2 is also sufficient.
Hence ans is D
Bunuel,
VeritasKarishma Please suggest if my method is correct. It took more than 2 mins to solve this question.
Please guide if any other shorter method or logic to solve this question