Peter's Trip

[GWS]

Peter makes a business trip from his house to Chicogo in two hours. One hour later, he returns home in traffic at a rate of 20 mph less than his rate going. If Peter is gone a total of 6 hours, how fast did he travel on each leg of the trip?

The book explains that Peter did not travel one of those hours, reducing his trip time from 6 hours to 5 hours.

Where in the question does it say that I should deduct 1 hour from 6? In any case, how do I solve this question?

I know that using rt = d will help me.

I also know that distances are equal in this question.

There are two rates: x and x - 20

Where do I go from here?

 

[Gene]

It says "One hour later, he returns home" so he wasn't driving for one hour and that hour doesn't count in his speed.
The two times are 2 and 5-2=3 so
x*(2)=(x-20)*3
2x=3x-60
x=60 mph going
x-20 = 40 mph returning

 

[GWS]

ok

Gene,

Thank you for your help. My problem has been setting up the proper equation from the given data in word problems. All students, some math tutors and a few math teachers have trouble setting up equations like the one you set up. This is a great skill to learn! Any suggestions? Should I practice word problems everyday? What is your view?

 

[Gene]

Well, avuncular advice.
Glance thru it, ignoring the story line.
Assign a variable to what seem to be the key factor. Pick one that recalls what it is. First letter of a name, d for distance, t, h, m for time hours or minutes,... Anything that works for you.
Take one sentence at a time that refers to that, adding other variables as necessary. This talks about his speed and time. You know d=rt so those are probably good ones to start with. It gives t=2 and 5-t for time to and from and there are two trips so you have started two equations
d=rt and
d=r(5-t)
You did fine that far except for x instead of r. The rates are given as r and r-20 so you have
d=rt and
d=(r-20)(5-t)
And you are almost done.
This one isn't too good for illustration. Most problems you can just replace one whole sentence with an equation.
(There is a problem with Topic review right now so I may be mixing things up.)

 

[GWS]

ok

Thank you for your explanation and for taking time out to help me.