[MOVED] How long to fill the jar using all four spouts?

[jennybenny02]

I can't figure out an equation for the following exercise that gives the answer supplied in my book. Any help would be GREAT! Thanks

A Brazen lion has 4 spouts (the two eyes, the mouth, and flat of the right foot). For the purposes of this exercise, "1 days" is twelve hours.

The right eye fills a jar in 2 days (that is, 24 hours). The left eye fills a jar in 3 days (36 hours). The foot fills a jar in 4 days (48 hours). The mouth is capable of filling the jar in half a day (6 hours).

How long will ALL four together take to fill the jar?

The answer given in my book is (144/37 hours)

 

[stapel]

Use the customary "work" problem set-up, converting the times into rates:

. . .time (in hours) to complete job:
. . . . .right eye: 24
. . . . .left eye: 36
. . . . .foot: 48
. . . . .mouth: ??
. . . . .together: t

. . .completed per time unit:
. . . . .right eye: 1/24
. . . . .left eye: 1/36
. . . . .foot: ??
. . . . .mouth: ??
. . . . .together: ??

Complete the table.

Add their input labors. Set the sum equal to what they accomplish together. Solve.

Eliz.

 

[jennybenny02]

Hmm.. Im still confused as to what Im supposed to do. I think I understand your table, but not sure how to make it work to know how long All 4 together take to fill the jar. I keep doing stuff to make common denominators or something but just keep getting stuck.....

 

[stapel]

I think I understand your table, but not sure how to make it work to know how long all 4 together take to fill the jar.

That's what the variable "t" is defined to stand for: the number of hours they take to complete the task when working together. Set up the equation according to the instructions, and solve for the value of the variable.

I keep doing stuff....

Please reply showing your work. Thank you.

Eliz.

 

[Denis]

In case you're having problems with lcd, you should get:
1/24 + 1/36 + 1/48 + 1/6 = 37/144
That's the filled portion of the jar after one hour.

Carry on...