Question

Tom can fix a car in 6 hours. Ellen can do it in 4 hours. How long would it tak them working together?

Answer 1

one way to think of these problems is
rate * time = job

(almost like rate * time = distance)

tom's rate is 1 job/6 hours (1 car per 6 hours)
ellen's rate is ¼

if you add them:
(1/6 + ¼) t = 1
can you solve for t ?

Answer 2

I would add 1/6 + 1/4? @phi

Answer 3

Let T be how fast Tom can fix the car alone
Let E be how fast Ellen can fix the car alone
Let x be how fast Tom and Ellen can fix the car together

Then

\[\frac{T \times E}{T + E} = x\]

Since in this case
T = 6
E = 4

Then
\[\frac{6 \times 4}{6 + 4} = x\]

Answer 4

24/10?

Answer 5

or 2.4 Hours in decimal form

Answer 6

Ok the answer in the book is 2 hrs 24 minutes. How did they get that?

Answer 7

Because they converted 4/10 of an hour to minutes

Answer 8

.4 = 4/10

Answer 9

You can set up a proportion such as this to find minutes:

\[\frac{4}{10} = \frac{x}{60}\]

Answer 10

If you have the fraction of hours, you can convert it to minutes by setting the hour fraction equal to the minutes fraction x/60

Answer 11

Then solve for x