# Time and Distance Problems Shortcuts Trick #3 Fast Math Trick

This type of question are asked in many competitive exams. Most of the students are not able to solve this question and some who are able to solve it have taken minutes to solve this question. But here we will tell you the trick to solve this type of question. That trick will solve this type of question in seconds. You just have to put the given terms into the formula and you will get the answer.
The question and the trick is explained below.
Q:- a person travels a total journey of 120 kms. He travels his half distance at a speed of 60 km/h and half of the remaining  at a speed of 30 km/h and the last remaining at a speed of 10 km/h. what is his average speed during the whole journey?

Now
D1=first half distance of 120 kms=60 km, speed=x=60km/h
D2=half of the remaining(60)=30 km, speed=y= 30km/h
D3=the last remaining=30 km, speed=z=10km/h

Tricky solution.
Here is a tricky rule for this type of question which will solve it very quickly.

Rule:- If three different distances D1, D2, D3 are travelled at 3 different speeds i.e. x,y,z respectively, then

Average speed=(D1+D2+D3)/{(D1/x)+(D2/y)+(D3/z)}     km/h

Average speed= (60+30+30)/ {(60/60)+(30/30)+(30/10)}     km/h

Average speed= 120/(1+1+3)=120/5    km/h

Average speed=24 km/h

So you can solve this type of typical question in just few seconds if you know the above formula trick.