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Help! Math word problem!

castel left the mall driving west one hour before dan. dan drove in the opposite direction going 40mph slower than castel for 3hours after which time they were 335miles apart. find castel's speed. 

When I looked at the web site my tewacher gave me to solve this it just gave me the formula: distance= rate x time.

I really need fast help.

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5 Answers

From the question we can tell that Dan drove for 3 hours. Castel left the mall one hour before Dan, so she drove for 4 hours. For convenience's sake, we say that Castel drives with a speed of x; in this case, Dan's speed is x - 40 (he drives 40mph more slowly).

Now we can set up the equation:

4x + 3 (x - 40) = 335;

4x + 3x - 120 = 335;

7x = 455;

x = 65.

Castel drives at 65mph.

Hey Brianna -- good hearing from "the Land Between the Lakes!"

Here's another angle you might like ... since we're aiming for a 335-mile gap, for the 1st hour I'm guessing Castel is going 55, 65, or 75mph, leaving 280, 270, or 260 miles to amass in last 3 hrs ... I like the "270" since you can cut it in three ... the 90mph difference has << 65mph for Castel and Dan at 25mph >> We now have 4x65 for C or 260 miles, and 3X25 for D or 75 miles making the total 335 ... Best wishes, ma'am  

If Castel's speed is x miles/hour then Dan's speed is x-40 miles/hour.  Castel drove for 4 hours and Dan drove for 3 hours in the opposite direction.  The sum of the two speeds equals 335 miles.

Castel's distance = x miles/hour * 4 hour.

Dan's distance =(x-40) miles/hour * 3 hours.

Notice for both equations hours cancels leaving you with only miles left. 

Castel's distance + Dan's distance = 335 miles

4x+3(x-40) = 335-------->4x+3x-120=335---------> 7x=455------>x=65 miles/hour=Castel's speed.

Assume Castel's speed is x mph, so Dan's speed is x-40.

So one hour after Castel left the mall, the distance between them is x*1=x.

After that Dan drove in the opposite direction, and after 3 hours, the distance between them increased by: (x+(x-40))*3, so the total distance is x+(x+(x-40))*3=335.

Simplify the left hand side of the equation above, we have:

7x-120=335

solve this equation, we have: x= 65 (mph)

The castel's speed is 65mph.

 

When it comes to distance/speed/time problems, I find it helpful to make a table of the information we know and need to find.

We know that Castel and Dan were a total of 335 miles. So if Castel drove some x miles, then Dan had to have driven 335 - x miles. We also know Dan drove 40 mph slower than Castel, so if we represent Castel's speed as y, we can represent Dan's speed as x - 40. And we know Dan drove for 3 hours, while Castel left an hour before him, so he drove for 4 hours.

                    DISTANCE               SPEED               TIME

Castel                 x                           y                 4 hours

Dan               335 - x                    y - 40              3 hours

Now we can make two formulas using the one you were given, distance = speed x time.

x = 4y

335 - x = 3(y - 40)

Since we are solving for y (Castel's speed), I'm going to plug 4y in for x (since they are equal based on the first equation) in the second equation.

335 - 4y = 3(y - 40)          Now I'm going to simplify and solve for y.

335 - 4y = 3y - 120

455 = 7y

y = 455 / 7 = 65 mph