Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

If I walk at 3 km/hr. I miss a train by 2 minutes , if however I walk at 4 km/hr then I reach the station 2 minutes before the arrival of the train .How far do I walk to reach the station ?
A) 34km
B) 45km
C) 54km
D) 1 km

Answer
VerifiedVerified
477.3k+ views
like imagedislike image
Hint:
Assuming x to the distance and using the relation time = distancespeedwe get the time as T=(x3+260)when I walk at a speed of 3 km/hr and T=(x4260) when I walk at a speed of 4 km/hr and equating these both we get the value of x.

Complete step by step solution:
Let x be the distance which I walk to reach the station
We know that time = distancespeed
Therefore when I walk at a speed of 3 km/hr I reach the station 2 minutes late
T=(x3+260) ……….(1)
Here the extra 2 minutes is written as 260because our calculation in done in terms of hours so we convert minutes to hours by dividing it by 60
Here we add the two minutes as I take two minutes extra (in addition )

 Therefore when I walk at a speed of 4 km/hr I reach the station 2 minutes early
T=(x4260) ……….(2)
Here we subtract the two minutes as I reach 2 minutes earlier
Equating (1) and (2)
(x3+260)=(x4260)x3x4=1301304x3x12=230x12=115x=1215=45km
Since distance cannot be negative
x=45km

The correct option is c.

Note:
If distance travelled for each part of the journey,
Ie d1=d2=....=dn=d, then the average speed of the object is Harmonic Mean of speeds.
Let each distance be covered with speeds s1,s2,...,sn in t1,t2,...,tn times respectively.
Then t1=ds1,t2=ds2,...,tn=dsn