• May 18th 2010, 07:09 PM
MickG86
Hi there,

I had the following question in a exam a couple of days ago and I couldn't solve it, but I know I had to use a Quadratic Equation (ax˛+bx+c). Still I didn't came up with a formula....

Question:
A journey from A to B is 550km. In my steady little car that travels at a nice sedate speed I get there in a reasonable time. However if I hired something more up market that travels on average 6km/hr faster (still keeping under the speed limit of course), I can get to B 50 minutes sooner.

Determine the average speed of my steady little car, and how long I will take to get to B.

Thank you for your help (Bow)
• May 18th 2010, 08:44 PM
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Quote:

Originally Posted by MickG86
Hi there,

I had the following question in a exam a couple of days ago and I couldn't solve it, but I know I had to use a Quadratic Equation (ax˛+bx+c). Still I didn't came up with a formula....

Question:
A journey from A to B is 550km. In my steady little car that travels at a nice sedate speed I get there in a reasonable time. However if I hired something more up market that travels on average 6km/hr faster (still keeping under the speed limit of course), I can get to B 50 minutes sooner.

Determine the average speed of my steady little car, and how long I will take to get to B.

Thank you for your help (Bow)

Hi, MickG86,

In general,

$\displaystyle x = v_{av}t$

So, let $\displaystyle v_s$ represent the slower speed, and $\displaystyle v_f$ represent the faster one, likewise $\displaystyle t_s$ and $\displaystyle t_f$. We have

$\displaystyle x = v_st_s$
$\displaystyle x = v_ft_f = (v_s+6)(t_s-5/6)$

Set them equal

$\displaystyle v_st_s = (v_s+6)(t_s-5/6)$

Solve for $\displaystyle t_s$ with the intent of substituting later on

$\displaystyle v_st_s = v_st_s-(5/6)v_s+6t_s-5$

$\displaystyle 6t_s = (5/6)v_s+5$

$\displaystyle t_s = (5/36)v_s+5/6$

Substitute

$\displaystyle x = v_st_s$

$\displaystyle x = v_s((5/36)v_s+5/6)$

$\displaystyle 36x = v_s(5v_s+30)$

$\displaystyle 36x = 5v_s^2+30v_s$

$\displaystyle 5v_s^2+30v_s - 36x = 0$

$\displaystyle 5v_s^2+30v_s - 36(550) = 0$

$\displaystyle v_s^2+6v_s - 3960 = 0$

Quadratic equation... (I'll leave that part to you)

Solution: $\displaystyle v_s = 60 \text{ km/h}$

Plug it back into

$\displaystyle x = v_st_s$

to get

$\displaystyle t_s = 9 \text{ hrs}, 10 \text{ min}$
• May 18th 2010, 09:11 PM
Wilmer
Code:

[1] A ....@ v ..........[550].............. B : h hours   [2] A ....@ v+6 ........[550].............. B : h-5/6 hours
[1] hv = 550
[2] (h-5/6)(v+6) = 550
• May 18th 2010, 09:57 PM
MickG86
Thank you (Happy)