Two friends are painting a living room. Ken can paint it in 6 hours working alone. If Barbie works alone, it will take her 8 hours. How long will it take working together? Round to the nearest tenth.

Question

Two friends are painting a living room.  Ken can paint it in 6 hours working alone.  If Barbie works alone, it will take her 8 hours.  How long will it take working together?  Round to the nearest tenth.

anonymous · Answer

i hated these problems when i was a kid :D but let me try

amistre64 · Answer

the idea is to determine how much work can be done in a given unit of time; in this case, say 1 hour

anonymous · Answer

never mind :)

anonymous · Answer

Two words: Harmonic mean

amistre64 · Answer

if K works at a steady rate, then in 1 hour, 1/6 of the room is painted

if B works at a steady rate, then in 1 hour, 1/8 of the room is painted

togehter in an hour they can paint 1/6+1/8 of the room

anonymous · Answer

Ken paints 1 room in 6 hours. 1/6
Barbie pains 1 room in 8 hours 1/8

1/6+1/8 = 8/48+6/48
=14/48 So they can pain 14 rooms in 48 hours so 48/14=3.428 hours.

Not sure if it's right.

amistre64 · Answer

6+8
---- is the work per hour ; if we flip that we get hours per work
6x8

lgbasallote · Answer

1/6 + 1/8 = 1/t

multiply everything by t...

t/6 + t/8 = 1
8t + 6t = 48
14t = 48
t = 24/7
t = 3.4 hours

amistre64 · Answer

two words harmonic mean is actually 4 words plus some to explain it :)

anonymous · Answer

Lol, okay you also need to multiply that by $\frac12$. This is a full answer!