Peter travels 20 km a day uniformly. John starts from the same point peter started after three days. He travels at a speed of 15 km a day on the first day, at 19 km a day of the second day and so on following an arithmetic progression.
In how many days will he catch up with Peter?
Solution:
John starts after 3 days, thus Peter has already covered 60 km by then (travelling at 20km a day)
The distance between Peter and John will be increased to 60 + 5 + 1 = 66 km in the next two days.
Since John is following an arithmetic progression in the speed daily, the distance between him and peter will keep on decreasing from the 6th day. It will decrease by 3 km on the first day, 7 km on the next day and so on.
Now John will catch up with Peter after n + 5 days from the start of Peter
Thus
66 = (n/2)*(2*3 + (n-1)*4)
If we solve for n in the above equation, we will get n = 5.5
Thus John will catch up with Peter on the eights day when he starts running after Peter.