want to check and see if I did this right.

[Cbrewer]

Fred can explore a house in 8 hrs. Ted can explore a house in 10 hrs. If there are 21 houses to explore, how long will it take Fred and Ted to explore them together?

My Work

Fred =8 hrs
8(21)= 168 hrs
It takes Fred 168 hours to explore 21 houses.

Ted = 10 hrs
10(21)= 210 hrs
it takes Ted 210 hrs to explore 21 houses.

Let h = time it took together to explore the houses.

h= 168 + 210/2
h= 378/2

h= 189 hrs
It takes Fred and Ted 189 hrs to search all the rooms together.

 

[DrPhil]

Fred can explore a house in 8 hrs. Ted can explore a house in 10 hrs. If there are 21 houses to explore, how long will it take Fred and Ted to explore them together?

My Work

Fred =8 hrs
8(21)= 168 hrs
It takes Fred 168 hours to explore 21 houses.

Ted = 10 hrs
10(21)= 210 hrs
it takes Ted 210 hrs to explore 21 houses.

Let h = time it took together to explore the houses.

h= 168 + 210/2
h= 378/2

h= 189 hrs
It takes Fred and Ted 189 hrs to search all the rooms together.

If you are very careful with units, you will see that this is a rate problem, which usually takes a "harmonic" average (that is, an average of reciprocals).

Fred's rate of exploration is 1 house per 8 hours, or 0.125 houses/hour
Ted's rate of exploration is 1 house per 10 hours, or 0.100 houses/hour

Added together, the rate is 0.225 houses/hour
[Alternatively, 1/R = 1/8h + 1/10h --> R = 1/[1/8h + 1/10h) = 4 4/9 h per house]

(21 houses)/(0.225 houses/hour) = 93 1/3 hours

 

[HallsofIvy]

I would have done this using fractions rather than decimals.

Fred's rate of exploration is "one house per eight hours" or 1/8 "house per hour".
Ted's rate of exploration is "one house per ten hours" or 1/10 "house per hour".

Together they work at a rate of 1/8+ 1/10= 5/40+ 4/40= 9/40 "house per hour" so that, together, they could do one house in 40/9 hours.
21 houses, then would require (21)(40/9)= 840/9 hours= 93 hours, 20 minutes.

How many days, weeks, months that will be depend upon how many hours a day and days a week they work!

(I can't help but wonder why they are searching houses! What are they looking for?)

 

[Dale10101]

Interesting

Fred can explore a house in 8 hrs. Ted can explore a house in 10 hrs. If there are 21 houses to explore, how long will it take Fred and Ted to explore them together?

My Work

Fred =8 hrs
8(21)= 168 hrs
It takes Fred 168 hours to explore 21 houses.

Ted = 10 hrs
10(21)= 210 hrs
it takes Ted 210 hrs to explore 21 houses.

Let h = time it took together to explore the houses.

h= 168 + 210/2
h= 378/2

h= 189 hrs
It takes Fred and Ted 189 hrs to search all the rooms together.

My conclusion. Ted must be rather entertaining. I mean if it takes Fred 168 hours to explore 21 houses, and together it takes them even longer, 189 hours, well, they must be having fun ! ;-)