i know sometimes googleplay store won't download or slow download or connection timeout(retry connect).
or sometimes you see your download speed too slow.
try my method i wish it will fix your problems:
first you should be rooted:
for google play fix ...you will need es file explorer(search in google if you don't have it).
open es file explorer >>press on menu key(option key in your phone)>>click on tools>>root explorer>>
mount r/w>>make (/) and /system >>>r/w.
then go to system directory>etc folder>there is file called hosts>>delete this file.(using es file explorer).
then on es file explorer >press on menu key(option key in your phone)>>click on tools>>root explorer>>
mount r/w>>make (/) and /system >>>r/o.(to protect system and prevent malware to enter system).
by this you will fix google play problem.
for internet speed fixyou don't need root):
from play store download and install :wifi settings (dns,ip,gateway).
then open it click on current dns and select open dns home .
after that click applay.
you are done.
i make this and worked for me(on galaxy s4 verizon on 4.4.2).