How do you solve this problem. a bat flying at 3.7m/s spots an insect 23.8 meters away. how much must the bat increase its speed to reach the bug in 1.8 seconds.

Here's how I would do it:

How far does he have to go to catch the bug ?  23.8 meters

How soon does he want to get there ?  1.8 seconds

What speed does he need ?  (23.8 m) / (1.8 sec) = 13.222 m/sec

What speed is he flying now?    3.7m/s

How much does he need to increase it ?  (13.222 - 3.7) =  9.5 m/s faster