Math Is Fun Forum

mathsux

Member

Registered: 2007-08-06

Posts: 10

1. Average Speed of the Car

The distance of two towns is 120km by road and 150km by rail. A train takes 10 minutes longer than a car whose average speed is 10km/h less than the train's average speed. The purpose of this problem is to find the average speed of the car.

a) Let the average speed of the car be x km/h and the time taken by the car be t hours. Show the information gives:

xt = 120 (1)
(x+10)(t + 1/6) = 150 (2)

b) Subtract (1) from (2) to obtain a linear equation linking x and t.

I have no idea how to do this.

Please Help. It will be on a test tomorrow.

-mathsux

Last edited by mathsux (2007-08-07 20:13:32)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 1. Average Speed of the Car

To get equations (1) and (2), you need to use the information you're given along with the fact that distance = speed x time.

The car's average speed is x and it takes t hours to reach the town, so the distance it has gone is xt. We're told that the town is 120km away by road, so xt = 120.

The train's average speed is 10km/h faster than the car's, that is, (x + 10).
The train takes 10 minutes (or 1/6 of an hour) longer to reach the town than the car does, so it takes (t + 1/6).
For the same reason as before, this means that (x + 10)(t + 1/6) = 150.

Before you take (1) from (2), you need to expand (2) first.

(x + 10)(t + 1/6) = 150
xt + 1/6x + 10t + 10/6 = 150.

Now we can take (1) away from this to give:
1/6x + 10t = 85/3.

Scale up to get rid of fractions: x + 60t = 170.
Rather nicely, if you measured time in minutes instead of hours, the equation would just be x + t = 170.

---

Why did the vector cross the road?
It wanted to be normal.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: 1. Average Speed of the Car

goddamnit, you posted while i was writing my post:

: deleted to stop duplicate

Last edited by luca-deltodesco (2007-08-07 20:32:32)

---

The Beginning Of All Things To End.
The End Of All Things To Come.

HallsofIvy

Guest

Re: 1. Average Speed of the Car

Don't you just hate when that happens?

  You post an absolutely brilliant solution to a problem, proving that you are the most intelligent person in the world, only to find that someone has already posted a (possibly better) solution before you!

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 1. Average Speed of the Car

Heh, sorry about that. Still, it happens to everyone.
If I'm writing a particularly long post, I sometimes hit "preview" halfway through to check on the topic review that appears below the post box. That way I can stop if someone has already answered.

---

Why did the vector cross the road?
It wanted to be normal.

mathsux

Member

Registered: 2007-08-06

Posts: 10

Re: 1. Average Speed of the Car

thanks..that sureeee helped