## anonymous 5 years ago During the first part of a trip, a conoeist travels 34 miles at a certain speed. The conoeist travels 6 miles on the second part of the trip at a speed of 5mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip?

1. anonymous

yeh, its very similar to all questions asked one use pronumerals to represent unknowns

2. anonymous

let the first speed be x

3. anonymous

then distance = rate x time

4. anonymous

time = distance/rate

5. anonymous

time for first section of trip is T1 = 34/x now, the speed they travel for second part of trip is (x-5) { 5mph slower} so time for second part = T2 = 6/ (x-5) and we are told that the total trip = 3hrs so the sum of the times = 3hrs

6. anonymous

$\frac{34}{x} + \frac{6}{x-5} = 3$

7. anonymous

solve for x,

8. anonymous

this gives 2 solutions x= 3.94 and x= 14.4

9. anonymous

now, the answer cannot be x=3.94 , because if we try to determine the speed of the second part of the trip then we would get a negative value ( remember the speed for second trip was (x-5)mph )

10. anonymous

therefore x=14.4mph is the speed for first section , and 9.4mph is the speed for the second section

11. anonymous

$\sqrt{9x+67}=x+5$

12. anonymous

what ?

13. anonymous

I need to solve....well see what the heck I did wrong anyway..

14. anonymous

then I have one more..if that is ok...then I will leave everyone alone...I hate that I get so confused

15. anonymous

square both sides 9x + 67 = x^2 +10x +25 x^2 +x +25-67 =0 x^2 + x -42=0 (x+7)(x-6) =0

16. anonymous

x=6, x=-7 but check your solns

17. anonymous

x=-7 doesnt work, so x=6 is only soln

18. anonymous

ok so one more if you have time?

19. anonymous

might as well, shouldnt take long

20. anonymous

Write a quadratic equation in the variable x having the given numbers as solutions. The equation is standard form, ax^2+bx+c=0 $-\sqrt{3}, 6\sqrt{3}$

21. anonymous

$(x+\sqrt{3}) ( x-6\sqrt{3}) =0$

22. anonymous

expand

23. anonymous

x^2 -6sqrt(3)x +sqrt(3)x -6sqrt(3)sqrt(3) =0 $x^2 - 6\sqrt{3}x - 18 =0$

24. anonymous

wait no

25. anonymous

$x^2 -5\sqrt{3}x -18 =0$ thats it

26. anonymous

if you have a quadratic eqn with roots a and b , then the formula for that quadratic is (x-a)(x-b) =0

27. anonymous

ok..thanks:)