Applications of Quadratics: J passes pt at 8 @ 50 kph, M at

[susan123]

Hi. I'm doing applications of quadratic equations in math. I can usually solve most word problems but the ones involving clock time are giving me a hard time. What I think should logically work doesn't.

ex: Jim passes an intersection at 8:00 am, traveling east at 50 km/h. At 11:00 am, Mary passes the same intersection traveling south at 80 km/h. Algebraically determine when the vehicles are 750 km apart (Write your answer in clock time).

This is what I did:

d = vt

x = time when they are 750 km apart.

d (Jim) = 50 (x-8)
d (Mary) = 80 (x-11)

Then I used Pythagoras' theorem.

750^2 = [50(x-8)]^2 + [80(x-11)]^2
562500 = 2500x^2 - 40000x + 160000 + 6400x^2 - 140800x + 774400
3900x^2 +180800x - 371900 = 0

then I used the quadratic formula

x = -180800 ± ? (180800^2 - 4 x 3900 x -371900)
2(3900)

x= (-180800 ± 196189) / 7800

x = 1.97 x = -1.97

I have no idea if that's even right or if it is, where to go from there. Could someone help please?

 

[fasteddie65]

Re: Applications of Quadratic Equations

I get 1.97 and -48.33. Obviously the negative answer is not reasonable in this situation.
So what do we do with 1.97? On my calculator, I have a key on my calculator DMS which changes radians to degrees. I used it and found that 1.97 = 1 hr 58 min and 22.6 sec.

 

[mmm4444bot]

Re: Applications of Quadratic Equations

... x = time of day (using a 24-hour clock) when they are 750 km apart.

Jim: d[sub:1yx05b3s]j[/sub:1yx05b3s] = 50 (x-8)

Mary: d[sub:1yx05b3s]m[/sub:1yx05b3s] = 80 (x-11)

750^2 = [50(x-8)]^2 + [80(x-11)]^2

562500 = 2500x^2 - 40000x + 160000 + 6400x^2 - 140800x + 774400

3900x^2 +180800x - 371900 = 0 This leading coefficient is not correct; check your arithmetic.

...

I altered your definition of the symbol x, since it was not clear. For the way in which you set up the equation, the correct solution for x will represent the number of hours past midnight. You will either need to interpret this value using a 12-hour clock or explicitly state that you are using a 24-hour clock when you report your final answer.

I put subscripts on the symbol d because the same symbol may not be used to represent two different quantities.

Fix your arithmetic mistake, and then apply the quadratic formula, again.

Let us know if you need any more help with this exercise; thank you for showing your work!

Oh, by the way, please stop using the letter x as a multiplication sign. Either use implicit multiplication with grouping symbols or use an asterisk to indicate multiplication.

EG:

16*x = 16x

(16)(x) = 16x

Cheers,

~ Mark