quadratic word problem

[Woodwindplayer]

This problem is supposed to require quadratics to solve it, but I don't get them when I setup the problem.

Two guys travel 300 miles. The first travels by train. The second leaves one hour later and travels by car. In order to arrive at the same time he drives 10 mph faster than the train. How long is the train trip?

I thought I would use the distance formula, with t for the trains time and r for its speed: 300 = rt
The car has two modifications: rate is r + 10 and time is t - 1, so I got: 300 = (r + 10)(t - 1)

If I combine the equations I get a mess that's not quadratic. I know the answer is 6 hours, I'm just not sure how to set it up.

 

[Denis]

You were almost there :shock:

rt = (t - 1)(r + 10) ; r + 10t - 10 = 0 [1]

rt = 300 ; r = 300/t [2]

Substitute [2] in [1]

 

[Woodwindplayer]

Thanks for the help. I knew I needed two equations to solve for the two variables, but I hit a brick wall. I have another one, but I want to see if I can muddle through it. :?