a train moves at a constant speed of 160 km/hr for 5 km and 64 km/hr for next 7 km. what is the average speed of the train ?
Answers
Average speed of the train is 60 km/hr.
Solution:
The given journey has two speed for two distances, therefore their average speed of train is calculated as follows,
Given: Total distance for the journey be d = 1 km + 1 km = 2 km
Speed for first 1 km = 120 km/h
Speed for second 1 km = 40 km/h
Time = \frac{Distance}{Speed}Time=
Speed
Distance
T_{1}=\frac{D_{1}}{S_{1}}=\frac{1}{120}T
1
=
S
1
D
1
=
120
1
And similarly time taken for the second speed = T_{2}T
2
T_{2}=\frac{D_{2}}{S_{2}}=\frac{1}{40}T
2
=
S
2
D
2
=
40
1
Total time taken for the journey: T=T_{1}+T_{2}T=T
1
+T
2
\begin{lgathered}\begin{array}{l}{\mathrm{T}=\frac{1}{120}+\frac{1}{40}} \\ \\{\mathrm{T}=\frac{1}{30}}\end{array}\end{lgathered}
T=
120
1
+
40
1
T=
30
1
Average speed = \frac{\text { Total distance }}{\text { Total time }}
Total time
Total distance
Average speed = \frac{2}{\frac{1}{30}}
30
1
2
Average speed = 2 \times 302×30
Average speed = 60 km/hr