Question

Help with part b pls thank u

Answer 1

Answer:

• See below

Step-by-step explanation:

• speed = distance / time
• time = distance / speed

a)

i)

Time taken at the first part:

• 105 / x

ii)

Time taken at the second part:

• (190 - 105) / (x + 12) =
• 85/(x + 12)

b)

If time is 3 hours and 15 minutes = 3 1/4 hours = 13/4 hours, the equation is:

• 105/x + 85/(x + 12) = 13/4
• 4(x + 12)*105 + 4(85x) = 13x(x + 12)
• 13x² - 604x - 5040 = 0

c)

Solve the equation:

• 13x² - 604x - 5040 = 0
• x = [604 ± √((-604)² + 4*13*5040) ]/26 =
•      [604 ± √626896]/26 =
•      [604 ± 791.77]/26
• x = (604 + 791.77)/26 = 53.68 km/h (taking positive root only)

d)

• 105/x = 105/53.68 h = 1.956 h = 1 h 0.956*60 min = 1 h 57 min (rounded)
• 85/(53.68 + 12) = 85/65.68 = 1.294 h = 1 h 0.294*60 min = 1 h 18 min (rounded)

Answer 2

Answer:

see below

Step-by-step explanation:

Let t = time (in hours)

a) i)  First 105 km of journey

$\mathsf{speed=\dfrac{distance}{time}}$

$\implies x=\dfrac{105}{t_1}$

$\implies t_1=\dfrac{105}{x}$

ii) Rest of journey

distance = 190 - 105 = 85 km

speed = $x+12$ km/h

$\mathsf{speed=\dfrac{distance}{time}}$

$\implies x+12=\dfrac{85}{t_2}$

$\implies t_2=\dfrac{85}{x+12}$

b)  3 hours 15 minutes = 3.25 hours

$\implies$  total time = $t_1+t_2=3.25$

$\implies \dfrac{105}{x}+\dfrac{85}{x+12} =3.25$

$\implies \dfrac{105(x+12)+85x}{x(x+12)} =3.25$

$\implies 105(x+12)+85x =3.25x(x+12)$

$\implies 105x+1260+85x =3.25x^2 +39x$

$\implies 3.25x^2-151x-1260=0$

multiply by 4:

$\implies 13x^2-604x-5040=0$

c)

$\textsf{quadratic formula} \ x=\dfrac{-b \pm\sqrt{b^2-4ac} }{2a}}$

$\implies x=\dfrac{604 \pm\sqrt{(-604)^2-4(13)(-5040)} }{2(13)}}$

$\implies x=\dfrac{604 \pm\sqrt{626896} }{26}}$

$\implies x = 53.68, x=-7.22$

(to 2 decimal places)

d) time ≥ 0, therefore, x = 53.68 only

Substitute x = 53.68 into the expression for $t_1$ and solve for $x$:

$\implies t_1=\dfrac{105}{53.68}=1.955912... \textsf{hours}=\textsf{1 hr 57 min}$