# Word Problem (Algebra?)

## Homework Statement

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?

## Homework Equations

Needs to be determined

## The Attempt at a Solution

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

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

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

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...

symbolipoint
Homework Helper
Gold Member
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.

HallsofIvy
Homework Helper
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...
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?

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?

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

.88 x 60 = 53.333

average speed = 53.33 mph

Is that right? Did I confuse the numbers?

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

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

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

.88 x 60 = 53.333

average speed = 53.33 mph

Is that right? Did I confuse the numbers?
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!)