While travelling from A to B, Raghav travels a quarter of the distance at 10km/h, the next quarter of the distance at 15km/h, the third quarter of the distance at 20km/h, and the final quarter of the distance at 30km/h. While travelling on exactly the same route, Manish travels for a quarter of the total time taken for his journey at 10km/h, the next quarter of the total time taken for his journey at 15km/h, the third quarter of the total time taken for his journey at 20km/h, and the final quarter of the total time taken for his journey at 30km/h. If the overall average speed of Raghav during his journey is given as ykm/h, and that of Manish is given as zkm/h, find the value of (z−y).
- A1.5
- B2.75
- C2.5
- D4
Solution & Step-by-step Explanation
1. For Raghav (Equal Distances):
Let each quarter of the distance be d. Total distance =4d.
Total Time (t
R
)=
10
d
+
15
d
+
20
d
+
30
d
Taking the LCM of denominators (60):
t
R
=d(
60
6+4+3+2
)=
60
15d
=
4
d
Average Speed (y)=
Total Time
Total Distance
=
d/4
4d
=16km/h
2. For Manish (Equal Time Intervals):
Let each quarter of the total time be t. Total time =4t.
Total Distance (d
M
)=10t+15t+20t+30t=75t
Average Speed (z)=
Total Time
Total Distance
=
4t
75t
=18.75km/h
3. Value of (z−y):
z−y=18.75−16=2.75km/h
Let each quarter of the distance be d. Total distance =4d.
Total Time (t
R
)=
10
d
+
15
d
+
20
d
+
30
d
Taking the LCM of denominators (60):
t
R
=d(
60
6+4+3+2
)=
60
15d
=
4
d
Average Speed (y)=
Total Time
Total Distance
=
d/4
4d
=16km/h
2. For Manish (Equal Time Intervals):
Let each quarter of the total time be t. Total time =4t.
Total Distance (d
M
)=10t+15t+20t+30t=75t
Average Speed (z)=
Total Time
Total Distance
=
4t
75t
=18.75km/h
3. Value of (z−y):
z−y=18.75−16=2.75km/h