Note: I'm not sure what do you mean by "weight 0.05 kg/L". I assume it means the mass per unit of length, so it should be "0.05 kg/m".
Solution:
The fundamental frequency in a standing wave is given by
[tex]f= \frac{1}{2L} \sqrt{ \frac{T}{m/L} } [/tex]
where L is the length of the string, T the tension and m its mass. If we plug the data of the problem into the equation, we find
[tex]f= \frac{1}{2 \cdot 24 m} \sqrt{ \frac{240 N}{0.05 kg/m} }=1.44 Hz [/tex]
The wavelength of the standing wave is instead twice the length of the string:
[tex]\lambda=2 L= 2 \cdot 24 m=48 m[/tex]
So the speed of the wave is
[tex]v=\lambda f = (48 m)(1.44 Hz)=69.1 m/s[/tex]
And the time the pulse takes to reach the shop is the distance covered divided by the speed:
[tex]t= \frac{L}{v}= \frac{24 m}{69.1 m/s}=0.35 s [/tex]
