4.A car travels the first third of a distance with a speed of 10 kmph, the second third at 20 kmph and the last third at 60 kmph. What is its mean speed over the entire distance?
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Let the total distance traveled be s.
Hence the time taken for first third of the distance= t
1
=
v
1
s/3
Similarly, the time taken for second third of the distance= t
2
=
v
2
s/3
and the time taken for last third of the distance= t
3
=
v
3
s/3
Hence the mean speed over the distance=
t
1
+t
2
+t
3
s
=
v
1
1
+
v
2
1
+
v
3
1
3
=18km/h
Hence the time taken for first third of the distance= t
1
=
v
1
s/3
Similarly, the time taken for second third of the distance= t
2
=
v
2
s/3
and the time taken for last third of the distance= t
3
=
v
3
s/3
Hence the mean speed over the distance=
t
1
+t
2
+t
3
s
=
v
1
1
+
v
2
1
+
v
3
1
3
=18km/h
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