In a 3600m race around a circular track of length 400m, the faster runner an
the start of the race. All the runners maintain uniform speed throughout t
race. If the faster runner runs at thrice the speed of the slowest runner,th
the time taken by the faster runner to finish the race is
Answers
Answer:
24 min
Explanation:
Let the speed of the fastest runner =
3
x
m/s
speed of the slowest runner =
x
m/s
Relative speed of the fastest runner with respect the slowest runner
=
3
x
−
x
=
2
x
When the fastest and slowest runners meet for the first time, fastest runner would have run 1 round (400 m) more when compared to the slowest runner.
i.e., in 4 min (240 sec), fastest runner run 400 m more when compared to the slowest runner.
400
2
x
=
240
5
2
x
=
3
x
=
5
6
Speed of the fastest runner
=
3
x
=
3
×
5
6
=
2.5
m/s
Time taken by the faster runner to finish the race
=
3600
2.5
=
1440
seconds = 24 minutes
Solution 2
in 4 min, fastest runner run 400 m more when compared to the slowest runner.
Speed of the fastest runner : Speed of the slowest runner = 3 : 1
Suppose slowest runner runs
x
km in 4 min
Then the fastest runner runs
3
x
km in 4 min
then
2
x
=
400
x
=
200
i.e., in 4 min, fastest runner run
3
x
=
600
m
i.e., in 1 min, fastest runner run
600
4
=
150
m
Time taken by the fastest runner to finish the race =
3600
150
=
24
min