# Math Help - Quadratic Equation!?

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 (ax²+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.

2. 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 (ax²+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.

Hi, MickG86,

In general,

$x = v_{av}t$

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

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

Set them equal

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

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

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

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

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

Substitute

$x = v_st_s$

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

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

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

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

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

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

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

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

Plug it back into

$x = v_st_s$

to get

$t_s = 9 \text{ hrs}, 10 \text{ min}$

3. 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

4. Thank you