We must first find the rate taken to cover 1500.0 m within 14 min and 34.56 sec. We can first convert the time into seconds and hence, we have time = 14(60) + 34.56 = 874.56 seconds.
Recall that
rate = distance/ time.
And using the given for the men's world record, we have
rate = 1500.0 m / 874.56s = 1.715 m/s
Now, to find the time taken to cover 0.350 miles, we can first convert the distance to meters then use the equation given below.
time = distance/rate
where distance is equal to 0.350(1609) = 563.15 m. Hence, we have
time = 563.15 / 1.715 = 328.37 s
From this, we can see that it will takes 328.37 seconds to cover 0.350 miles.
Answer: 328.37 seconds
