Math New Drill (Level 2) : Velocity SNJ00-0404-L2 Distance between home and station

Taro left the house for the station and Jiro left the station for the house simultaneously. 

Both of 2 people walked by a fixed speed respectively. 

The distance between two persons was 632 m 5 minutes after leaving and it was 112 m 13 minutes after leaving. 

Find the possible distances between the house and the station.



Answer
957 m,
1097 m

Solution
Case1 : 
When 2 people didn't pass each other in 8 minutes during 13 minutes later from 5 minutes later. 

Because the distance 2 people moved in 8 minutes was 632 - 112 = 520m, the total speed per minute of 2 people is 520 / (13 - 5) = 65m/min. 

Therefore the distance between the house and the station is 632 + 65 × 5 = 957 m. 

Case 2 : 
When 2 people passed each other in 8 minutes during 13 minutes later from 5 minutes later. 

Because the distance 2 people moved in 8 minutes was 632 + 112 = 744m, the total speed per minute of 2 people is 744 / (13 - 5) = 93m/min. 

Therefore the distance between the house and the station is 632 + 93 × 5 = 1097 m.