Question

Three students entered a race around a track. Student- 1takes 6 minutes to run one lap.
and student - 2 takes 3 minutes and student- 3 takes 5minutes to complete one lap.
If all three students begin the race at the same time, how many minutes will it take for
all students to be at the starting point again?

Answer 1

Step-by-step explanation:

Consider that A takes t

1

second, then according to the given problem, B will take (t

1

+t) seconds. Further let v

1

be the velocity of B at finishing point, then velocity of A will be (v

1

+v). Writing equations of motion for A and B

v

1

+v=a

1

t

1

....(i)

v

1

=a

2

(t

2

+t) ....(ii)

From equations (i) and (ii), we get

v=(a

1

−a

2

)t

1

−a

2

t .....(iii)

Total distance travelled by both the cars is equal

S

A

=S

B

⇒

2

1

a

1

t

1

2

=

2

1

a

2

(t

1

+t)

2

⇒t

1

=

a

1

−

a

2

a

2

t

Substituting this value of t

1

in equation (iii), we get

v=(

a

1

a

2

)t