math word problem...?
A baker can decorate the day's cookie supply four times as fast as his new assistant. If they decorate all the cookies working together in 16 minutes, how long would it take for each of them to decorate the cookies working individually?
Comments
let the assistant can decorate in x minutes
so in 1 minute the assistant can decorate -------1/ x part
in 1 minute baker can decorate --------------------4/x part
so in 1 minute both together can decorate ----(1/x) + (4/x) = 5/x part
Both to gether can complet in ----------x /5 miutes
so x / 5 = 16
x = 80
Assistant can decorate individually in 80 minutes
The baker can decorate individually in 80/4 = 20 minutes
ok its been a long time since I've done this stuff. I made things easy tho. I said that each min the baker did 4 cookies and the assistant did 1 for 5 cookies a minute. Then I multiplied that by 16(min) for a total of 80 cookie for the day.
With that info I found that it would take the baker only 20 min. While it would take the assistant 80 min.
Depends on how long it it take the baker to decorate a cookie
If the helper takes 16 minutes to decorate '1' cookie (it's one of those big cookies), the baker can decorate 4.
If the helper decorates '2' cookies, then baker can decorate 8.
If the helper decorates '4' cookies, then baker can decorate 16. (These cookies are smaller.)
If the helper decorate '6' cookies, then baker can decorate 24.
(Yep ... even smaller.)
4 minutes for assistant because 4 times 4 = 16. But added together that's 18 minutes total (4 minutes for assistant and 16 minutes for baker). 3 minutes is too little. Somewhere in between.
1/5 of the work = assistant
1/5 work in 16 minutes
full work in 16*5=80 minutes = 1 hr 20 minutes. (assistant alone)
4/5 of the work=baker
4/5 in 16 minutes
1 in 16*5/4=20 minutes. (baker alone)
the baker would take 12.8 min
and the assist will take 3.2
you have to divide 16 by 5 to get the assistants time
Let the time taken by assistant=x
Time taken by baker=4x
total time=x+4x=5x
Given, 5x=16*60 seconds
5x=960 seconds
x=192 seconds
So,assistant can do it in 192 sec & baker can do it in 768 sec
Baker: 3.2 minutes
Assistant: 12.8 minutes
3 mins.