# Thread: Problem Solving with Quadratics

1. ## Problem Solving with Quadratics

Can any1 help me with these problems - i cant see to work them out :S

1. Find the width of a uniform concrete path placed around a 30m by 40m rectangular lawn given that the concrete has area on quarter of the lawn?

2. If the average speed of an aeroplane had been 120kmph less, it would have taken a half an hour longer to fly 1000km. Find the speed of the plane?

3. A group of elderly citizens hire a bus for $160. At the last minute 8 of them miss the trip due to illness. Therefore the other citizens had to pay an extra$1 each - how many elderly citizens went on the trip?

Thanks, much appreciated

2. 1. Here's the beginning of some working, hopefully I've interpreted the question correctly! :P

$A(lawn)=30 \times 40 = 1200m^2$
$A(total)=1200 + (1/4 * 1200) = 1500m^2$

Width of the path = x

$1500=(30+2x)(40+2x)$

Can you take it from there? (Remember, width must be positive)

2. t = time take and s = average speed of the aircraft
$t=1000/s$
$1000=s*t$
$1000=(s-120)((1000/s)+.5)$
$1000=.5s-(120000/s)+940$

Can you take it from there? (Remember, speed, a scalar quantity, must be positive)

3. $160=x \times c$ where x = number of seniors and c = cost per person
$160/x = c$
$160=(x-8)((160/x)+1)$
$160=x-(1280/x)+152$

Can you take it from there? (Remember, x must be a positive number)

3. Im still confused. The answer is 2.03 so im not sure what to do from (30 +2x)(40+2x) do u expand it out or?

And do you know anything about the other 2 questions?

4. I just expanded my original post to include the other two questions..

So therefore,
$1500=4x^2+140x+1200$
$0=4x^2+140x-300$

Can you solve quadratics like this?

5. Ahh cheers

Yeah i kinda got to thhe stages you had above i just wasn't too sure on them and on how to go from there to get the solutons but ive done them now

thanks very much

6. Just one more question, on the first 1, how did u get from

1200 + 1200/4 = 1500

To

1500 = (30 + 2x)(40 + 2x)

Thank u very much

7. Also posted here.