Question

How to do answer 16, 19 and 21? Please show me the solutions. ​

Answer 1

Answer:

The speed in still air =  200 mph.

Step-by-step explanation:

21.

If the speed of the plane in still air is  x mph then with the wind its speed is x+20 mph and against the wind it is x - 20 mph. Also let t hours be the time taken for the journey with the wind.

So we have the 2 equations:

x + 20 = 396 / t

x - 20 =  396 / (4 - t)

Subtracting to eliminate  x

40 =   396 / t - 396 / (4 - t)

40t(4 - t) = 396(4 - t) - 396t

160t - 40t^2 = 1584 - 396t - 396t

-40t^2 + 952t  - 1584 = 0

Dividing through by 8:

-5t^2 + 119t - 198 = 0

Using the quadratic formula we get t = 22,  1.8 hours . We ignore the 22 because  the total time is 4 hours.

So the speed x =  is found by plugging in t  1.8:

x + 20 = 396/1.8

x =  200 mph.

Answer 2

Answer:

16) the boy is 11 years old

Step-by-step explanation:

16) Let the boy’s present age be b.

b+5 = 4(b-9)^2, or

b+5 = 4[b^2–18b+81] = 4b^2–72b+324, or

4b^2–73b+319 = 0, or

(4b-29)(x-11) = 0, or

b = 11 or 7.25 years. The second value is inadmissible.

So the boy is 11 years old, now.