# Math Help - Word Problem

1. ## Word Problem

Hey all, this question has been bugging me for two days, it feels like i can see the solution but i can't quite put my finger on it.

1.) A car travels half the distance of a journey at an average speed of 80km/h and half at an average speed of x km/h.

Define a function, S, which gives the average speed for the total journey as a function of x.

2. Originally Posted by andrew2322
Hey all, this question has been bugging me for two days, it feels like i can see the solution but i can't quite put my finger on it.

1.) A car travels half the distance of a journey at an average speed of 80km/h and half at an average speed of x km/h.

Define a function, S, which gives the average speed for the total journey as a function of x.

Maybe I do not understand you correctly, but if half the journey was at 80 km/h and the other half at $x$ km/h, then wouldn't it simply be:

$S = \frac{80 + x}{2}$

Which if you want to write as a function of $x$ can be written as:

$x = 2S - 80$

3. ## hey

hello, that was my initial intention however, it was wrong, wrong and wrong again.

I've tried so many different ways of working it, its so frustrating!!

4. Let the total distance travelled is D

So time taken while travelling with 80kmph = $\frac{D}{160}$
and time taken by travelling with x kmph = $
\frac{D}{2x}

$

Function is given by

$
Avg~ Speed ~=\frac{Total~Distance}{Total ~Time}= \frac{D}{\frac{D}{160} + \frac{D}{2x}}
$

Go ahead cancel D and simplify

5. Originally Posted by janvdl
Maybe I do not understand you correctly, but if half the journey was at 80 km/h and the other half at
$x$ km/h, then wouldn't it simply be:

$S = \frac{80 + x}{2}$
not true in this case
It won't be correct
Never try to average the averages

6. ## hey

THATS EXACTLY WHAT I DID! well... several times atleast, then i tried many, MANY different other methods and they were all wrong too.

7. Originally Posted by andrew2322
THATS EXACTLY WHAT I DID! well... several times atleast, then i tried many, MANY different other methods and they were all wrong too.