Three metal rods are located relative to each other as shown in the figure below, where L3 = L1 L2. The speed of sound in a rod is given by v = sqrtY/ρ , where Y is Young's modulus for the rod and ρ is the density. Values of density and Young's modulus for the three materials are

ρ1 = 2.70 103 kg/m3, Y1 = 7.00 1010 N/m2,

ρ2 = 1.25 104 kg/m3, Y2 = 1.60 1010 N/m2,

ρ3 = 8.80 103 kg/m3, Y3 = 1.20 1011 N/m2.

If L3 = 1.50 m, what must the ratio L1/L2 be if a sound wave is to travel the length of rods 1 and 2 in the same time interval required for the wave to travel the length of rod 3?

photo: https://gyazo.com/ce2aa9c0658f31350613fcfcc4a15677

so far i have found the speed of sound for each member.

L1= 5091.751

L2= 1131.3708

L3 = 3692.7447

and it takes sound .000406201923 seconds to go through L3

i have so far tried graphing L1 L2=L3 and then using 1 1=.000406... to find intercepts but that got me nowhere. since the answer seems to only be on cheg, i don't have any clue where to even go from here. any help would be appreciated!