Question

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?

Answer 1

yeh, its very similar to all questions asked one

use pronumerals to represent unknowns

Answer 2

let the first speed be x

Answer 3

then distance = rate x time

Answer 4

time = distance/rate

Answer 5

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

Answer 6

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

Answer 7

solve for x,

Answer 8

this gives 2 solutions

x= 3.94 and x= 14.4

Answer 9

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 )

Answer 10

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

Answer 11

\[\sqrt{9x+67}=x+5\]

Answer 12

what ?

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

x=6, x=-7

but check your solns

Answer 17

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

Answer 18

ok so one more if you have time?

Answer 19

might as well, shouldnt take long

Answer 20

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

Answer 21

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

Answer 22

expand

Answer 23

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

Answer 24

wait no

Answer 25

\[x^2 -5\sqrt{3}x -18 =0 \]

thats it

Answer 26

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

Answer 27

ok..thanks:)