Time and Distance

Basic Formula:
Distance = Speed * Time
Average Speed = 2 x y / (x+y) Kmph.
Average Speed =  3 x y z / ( xy + yz+zx) Kmph


TRICK 1: When 2 different speeds are given and total time taken to cover the entire distance is given, then we can find the distance from one side by this formula-
Distance from one end =(Product of two speeds)*(Total time taken)/(Addition of two speeds)

Example :
A girl goes to school with the speed of 6km/hr and returns with the speed of 5 km/hr. If she takes 5.5 hours in all then the distance in km between her house and school is:

1. 30 kms 
2. 15 kms 
3. 32.5 kms
4. 27.5 kms

Solution- Now, the speeds are 6 km/h and 5 km/h and the total time taken is 5.5 hours.
The distance from college to house can be calculated by putting the values in the formula mentioned above.
Required Distance= (6*5) * 5.5/ (6+5) = 15 kms.
Note : distance for both the speeds being same so entire distance is twice the distance from one side.

TRICK 2: When 2 different speeds are given along with 2 different arrival times, then the distance can be found by 
Required Distance = (Product of the speeds)*(Difference between the arrival times) / (Difference of the two speeds)

Distance =  S1 *S2 *(diff of time ) / (S1~ S2)

Example:
A boy covers a certain distance between his college and house on bike. He reaches 10 minutes late to his college when he is having an average speed of 30 km/hr. However, with a speed of 40 km/hr, he reaches his college 5 minutes earlier. Find the distance between his house and college.

1. 20 km   
2. 40 km
3. 30 km 
4. 25 km 

Example :

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:

Solution: 

Let x= 64 km/hr and y = 80 km/hr

Average speed = (2xy) / (x+y)

                        = 2*64*80/ (64+80)

                           =10240/144 = 71.11 km/hr