If Tanmay covers three equal distances at the speeds of 2km/h, 3km/h and 4km/h, respectively, then find his average speed (in km/h) during the whole journey. (Rounded off to 2 decimal places)
- A3.25
- B5.75
- C4.35
- D2.77
Solution & Step-by-step Explanation
Let each equal distance be dkm.
Total distance covered = d+d+d=3dkm
Time taken to cover the distances at speeds 2km/h, 3km/h, and 4km/h respectively:
t
1
=
2
d
,t
2
=
3
d
,t
3
=
4
d
Total Time=
2
d
+
3
d
+
4
d
To add these fractions, find the LCM of 2, 3, and 4, which is 12:
Total Time=
12
6d+4d+3d
=
12
13d
hours
Now, compute average speed:
Average Speed=
Total Time
Total Distance
Average Speed=
12
13d
3d
=
13
3×12
=
13
36
≈2.77km/h
Total distance covered = d+d+d=3dkm
Time taken to cover the distances at speeds 2km/h, 3km/h, and 4km/h respectively:
t
1
=
2
d
,t
2
=
3
d
,t
3
=
4
d
Total Time=
2
d
+
3
d
+
4
d
To add these fractions, find the LCM of 2, 3, and 4, which is 12:
Total Time=
12
6d+4d+3d
=
12
13d
hours
Now, compute average speed:
Average Speed=
Total Time
Total Distance
Average Speed=
12
13d
3d
=
13
3×12
=
13
36
≈2.77km/h