Answer
$254s$
Work Step by Step
We can find the required time as follows:
$f_1^{\prime} v-f_2^{\prime}v=f_1^{\prime} u+f_2^{\prime}u$
This can be rearranged as:
$u=(\frac{f_1^{\prime}-f_2^{\prime}}{f_1^{\prime}+f_2^{\prime}})v$
We plug in the known values to obtain:
$u=(\frac{460-410}{460+410})(343)$
$u=19.7m/s$
Now $t=\frac{d}{u}$
We plug in the known values to obtain:
$t=\frac{5.0\times 10^3}{19.7}$
$t=254s$
