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### Distance, Rate and Time

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Date: 3 Jun 1995 16:16:54 -0400
From: Richard Seguin
Subject: Question on Distance, Rate and Time.

I have a question like this:

Ian travelled by train at 80km/h and then by car at 90 km/h. It took him 3 h
to travel the total distance of 265km.

Ok, what I did was:

Train:

Speed = 80km/h
Time = X

(80)(x)=80x

Car:

Speed: 90km/h
Time 3-X

80x = 90 (3-x)
80x=270 - 90x
170x=270
x= 1.5

Train's Distance was 120 Km and it's time was 1.5H
Car's Distance was 145km and it's time was 1.5H

Is what I did right? Please reply ASAP! Before 8 EST would be appreciated.

Richard Seguin
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Date: 6 Jun 1995 09:31:57 -0400
From: Dr. Ken
Subject: Re: Question on Distance, Rate and Time.

Hello there!

>Ian travelled by train at 80km/h and then by car at 90 km/h. It took him 3 h
>to travel the total distance of 265km.
. . .

>Car:
>
>        Speed: 90km/h
>        Time 3-X

I like this much.  However, I think your next step isn't quite right.  You
say that the two distances 80x and 90(3-x) are equal, but I don't think we
know that Ian travelled the same distance by each mode of transportation.

Instead, use the total distance 265 to make the equation

265 = 80x + 90(3-x)             since the two distances add to 265
265 = 80x + 270 - 90x
10x = 5
x = .5

So it looks like Ian traveled 1/2 hour by train, and then 2.5 hours by car.
That means he went 40 km by train, and the remaining 225 km by car.  Sound
good?

-K
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