If Lo can paint a house in 4 hr and Jo can paint the house in 6 hr How long will it take together? Why 2hr 24?

Question

I know the answer however how do I get to that answer??

Answer 1

the formula here is 1/(total time) = 1/x +1/y
so...
=> 1/4 +1/6 = 1/(total time)
=> 5/12 = 1/(total time)
get the (total time) by manipulating the equation... (cross multiplying)

=>5(total time)= 1 (12)
=>(total time)= 12/5
simplify 12/5 hours as mixed fraction it will become
2 and 2/5 hours or 2.4 hours

since we have 60 minutes in 1 hour we need to multiply .4 with 60 giving us a product of 24

so the final answer is 2 hours and 24 minutes.

Answer 2

1/6 + 1/4 = 1/job
(2 + 3)job = 12

job = 12 / 5

= 2 2/5 hr = 2hr and 24 minutes

Answer 3

Let area to be painted = X m ²
Lo `s rate of painting = X / 4 m ² / h
Jo`s rate of painting = X / 6 m ² / h
Working together they paint in 1 hour
X / 4 + X / 6 m ²
3X / 12 + 2X / 12 m ²
5x / 12 m ²
Time = Area / rate
Time = X / (5X / 12) h
Time = 12/5 h
Time = 2 2/5 h
Time = 2 h 24 min

Answer 4

let x= the number of hours that Lo and Jo can paint the house together.
Then , 1 hour of painting by Lo alone plus 1 hour of painting
by Jo alone is equal to the part of the house painted when Lo and Jo paint together for one hour..

Algebraically, 1/4 + 1/6 = 1/x
multiply LCD 12x, 3x + 2x = 12
5x = 12
x = 2.4 hr.
0.4 hour = 0.4 x 60 (minutes in 1 hr)= 24 minutes
Hence, time to paint the house together is 2 hr. and 24 minutes.

Answer 5

try to make both in the same time
so
Lo can paint the house in 4 hrs
so in 1 hour he will paint 1/4 of the house
Jo can paint in 6 hours
so he will pint in hour 1/6 of the house
so if both worked together
in hour they will paint 1/6+1/4 of the house =10/24=5/12 of the house
so they need 12/5 of hours to paint the house together
12/5 = 2 2/5 = 2hours & 24 min

Answer 6

rate together
= 1/4 + 1/6
= 5/12 house/hour
= 1/2.4 house/hour

2.4 hours
= 2 hour 24 minutes

Answer 7

you can make an analogy of a physics problem. each one paints in some speed
speed = distance / time
time = distance/speed
distance is an analogy for the house
if they are gonna paint together the same house, their speeds are gonna be summed.
speed of Lo = distance/4
speed of Jo = distance/6
the new time will be
new time = distance/(new speed)
new time = distance/(speed of Lo+speed of Jo)
new time = distance/(distance/4 + distance/6)
new time = 1/(1/4 + 1/6)
new time = 2,4h, that is, 2h24min