Kill background process when another process ends

I have a little question and I hope someone can help me because I can not find a proper solution.

I want to resolve a hostname; while waiting for the result, I'd like to print a notification if it takes more than 30 seconds with shell script commands, preferably built-ins or ubiquitous system commands.

I have a background process that sleeps and then prints a message; while sleeping, the process runs ping, but I can't figure out how to kill the background process after the ping finishes and the message keeps printing even if the ping ends prior to the 30 second time limit since this is part of a bigger script that takes some time to run.

Here's the code that I've been using:

((sleep 30; echo "Querying the DNS server takes more than 30 seconds.") & ping -q -c 1 localhost >/dev/null)

I would greatly appreciate any and all help. Other solutions are welcome too; I just want to tell the user that the DNS is too slow and this will affect the further execution. I have tried ping -w or -W but this is not measuring the resolution time. I have tried to trap the result from the ping. I have tried to kill all processes with the same GPID but it is killing the console also. I am not the best with scripts, maybe this is the reason why this takes me so much time. Thank you in advance.

I hope this approach helps you. I think everything is pretty much portable, except for "bc" maybe. I can give you a "bc-less" version if you need it. Good luck!

 #!/bin/bash

timeout=10; ## This is how long to wait before doing some batshit!
printed=1; ## this is how many times you want the message displayed (For  #instance, you might want a message EVERY X seconds)                        
starttime="$( date +%F ) $( date +%T.%3N )"

################### HERE GOES YOUR BACKGROUND PROCESS
sleep 30 &
#######################################################
processId=$!  ## And here we got the procees Id
#######################################################

while [ ! -z "$( ps -ef | grep $processId | grep -v grep )" ]
do
    endtime="$( date +%F ) $( date +%T.%3N )";
    timeelapsed=$( echo " $(date -d "$endtime" "+%s" ) - $(date -d "$starttime" "+%s" ) " | bc );
    if [[ ($timeelapsed -gt $timeout) && ($printed -ne 0) ]]
    then
            echo "This is taking more than $timeout seconds";
            printed=$(( printed - 1 ));
            starttime="$( date +%F ) $( date +%T.%3N )"
      fi
done


  ### Do something once everything finished
  echo "The background process ended!!"