another algebra thing...?

Question

dorothy drives 10 miles, then increases her speed by 10 miles/hour and drives another 25 miles. find her original speed if she drives for 45 mins.(pls give me with the quadratic equation...tnxÜ)

Answer 1

let the original speed be x miles/hr.

then, time taken in travelling 1st 10 miles=10/xhr

Now, increased speed=(x+10) mph

Hence, time taken in travelling for 25 miles={25/(x+10)}hr

total time elapsed=10/x+25/(x+10)hr=(35x+100)/x(x+10)

Given, (35x+100)/x(x+10)=0.75 (Since, 45 min=0.75hr)

i.e. 0.75x^2+7.5x=35x+100

i.e. 0.75x^2-27.5x-100=0

upon factorising, (0.75x+2.5)(x-40)=0

which gives x=40 miles/hr.
as the other factor gives a negative unacceptable value.

Answer 2

Take
Dorothy's Original Speed = x miles / min
Time taken to cover 10 miles = 10/x minutes ... (1)
Dorothy's new speed = x + 10/60 = x + 1/6 miles per minute
Time Taken to cover the next 25 miles = 25 divided by (6x+1 divided by 6) minutes.... (2)

Total time taken = (1) + (2) above = 45 minutes

= 10/x + 25 / (6x+ 1 divided by 6)

= 10/ x + (150 divided by 6x+1)

Simplifying we get

30x sqare minus 33x +2 = 0

Solving it for x, we can find Dorothy's original speed / minute.

Multiplying it by 60, we can find Dorathy's original speed in mile per hour

Okay?

Answer 3

Let her initial speed be X miles/hour.
Time taken for first 10 miles=10/X hours
Time taken for next 25 miles=25/(X+10)hours
Total time=45 min=0.75 hours
The equation therefore is as under.
10/X+25/(X+10)=0.75 simplifying we have
10(X+10)+25X=.75X(X+10)
X+10+2.5x=.075X^2+.75X
.075X^2-2.75X+10=0

Answer 4

speed(s) = distance(d)/time(t)

s1 = 10/t1 s2 = s1 + 10 = 25/t2

t1 = 10/s1 t2 = 25/(s1 +10)

t1 + t2 = 45 mins

therefore...

10/s1 + 25/(s1 + 10) = 45 (x S1)

10 + 25s1/(s1 + 10) = 45s1

10 + 25s1 = 45s1^2 + 450s1

--> 45s1^2 + 425s1=10 where s1 is the original speed and
^ is to the power of


i hope u get it ;)

Answer 5

10r + 25(r+10)= 35/.75
10r +25r + 250 = 46.667
35r = -203.33
r = -5.81mph

Answer 6

3x2-110x-400=0 is the equation
3 x square -110x-400=0

Answer 7

sorry cant help