# Word Problem (Algebra?)

1. Apr 27, 2008

### LLS

1. The problem statement, all variables and given/known data

It took Bill 1.5 times as long to drive to work as it took him to drive home. If the trip was 60 miles in each direction, and the total drive time round trip was 3 1/3 hours, what was Bill's average speed in mph on the way to work?

2. Relevant equations

Needs to be determined

3. The attempt at a solution

I am at a loss of how to setup the equation.

2. Apr 27, 2008

### Gallileo

Have you tried writing out what you are given first? :P

3. Apr 27, 2008

### LLS

I don't know how to set it up.

Work = 1.5 x Home

Work + Home = 3 1/3 hours

???

I don't know how to do this...

4. Apr 27, 2008

### symbolipoint

Set Up the solution this way:

Columns for rate, time, distance; rows for ToWork and FromWork. Fill in the information according to the given facts. Your unknowns which are proportianal to eachother, are the rates.

5. Apr 27, 2008

### HallsofIvy

Staff Emeritus
One of the things I would object to is that you haven't told us what "Work" and "Home" mean so that we cannot say whether it is right or not.

Of course, I understand that "Work" really mean "time required to drive to work" and "Home" is "time required to drive home from work". Yes, those two equations do represent what you are told: W= 1.5H and W+ H= 4/3 (I have shortened them a little).
If you replace "W" in the second equation by "1.5H", what do you get? Once you know what "W" is, you know how long it took him to drive to work. How far did he drive in that time? What was his average speed?

6. Apr 27, 2008

### LLS

1.5H = 4/3 -----> .88

.88 x 60 = 53.333

average speed = 53.33 mph

Is that right? Did I confuse the numbers?

7. Apr 27, 2008

### kamerling

It's actually W+H = 10/3. substitute W = 1.5H in that. W is the time in hours he took to get to work. To get a speed from that you use

$$speed = \frac {distance}{time}$$

8. Apr 27, 2008

### Dr Zoidburg

Just a little. It wasn't helped by HoI using the wrong number! (it should read 10/3 not 4/3 - the 4/3 is correct but HoI skipped a line). Also you're only / by H in your equation whereas you should be / by W + H.

Here's how I'd do it:
Let's call the time taken to drive home x.
Time taken to drive to work is 1.5 times the trip home, making it 1.5x
So total time driving is:
to home (x) + to work (1.5x) = 2.5x
total time taken in minutes is (3 1/3)*60 = 200 minutes (I find it's easier to work out than using fractions of hours)

From there, you should be able to work out how long it took Bill to drive home (x) and thus how long it took him to drive to work (in minutes). Then divide that by 60 to get number of hours it took him and the rest is simple (hint: It is a whole number!)