Answer:
The distance of the winning post is [tex]120m[/tex].
Therefore, option d) [tex]120m[/tex] is correct.
Step-by-step explanation:
Given,
The speed of A is [tex]1\frac{1}{3}[/tex] as fast as B.
The race ends in a dead heat, i.e., the time taken is the same.
Let the speed of B = [tex]Q[/tex] m/s
Therefore,
The speed of A = [tex]Q \times 1\frac{1}{3}[/tex] = [tex]\frac{4Q}{3}[/tex] m/s
Now,
Let the distance to the winning post for A = [tex]x[/tex] m
As given, the distance to the winning post for B = [tex](x-30)[/tex] m
As we know,
- Speed = [tex]\frac{Distance}{time}[/tex]
- Time = [tex]\frac{Distance}{speed}[/tex]
For A,
- Time = [tex]\frac{x}{\frac{4Q}{3} }[/tex] = [tex]\frac{3x}{4Q}[/tex] -------equation (1)
For B,
- Time = [tex]\frac{x-30}{Q} }[/tex] -------equation (2)
On comparing both the equations, we get:
- [tex]\frac{3x}{4Q} = \frac{x-30}{Q}[/tex]
- [tex]\frac{3x}{4} = x-30[/tex]
- [tex]3x= 4x- 120[/tex]
Therefore, the distance of the winning post is [tex]120m[/tex].