Question

23. Arvind is planning an expedition. He investigates three possible routes.
.
If he travels on route A, which is 800 km long, he expects to cover x km per day,
Route B, which is the same distance as route A, has more difficult conditions and he
would only expect to cover (x - 5) km per day.
Rote C, which is 100 km longer than route A, has easier conditions and he would
expect to cover (x + 5) km per day.
Route A
Route B
Arvind
Route C
(i) If route C takes 20 days less than route B, form an equation in x and reduce it to the
standard form.
(11) Find the number of days that he expects to take on route A.
that the noint (af), 6-, –a) and (-a13, av3) are the vertices of an equilateral
V​

Answer 1

(i)x²+5x-450=0

(ii)Therefore $\frac{800}{18.86} =42.41$ days that he expects to take on route A.

Step-by-step explanation:

Given , Arvinnd travels on route A, which is 800 km long, he expects to cover x km per day.

Time= distance/ speed

Time = $\frac{800}{x}$ day

Route B, which is same distance as route A, he would expect to cover (x-5) km per day.

Time =$\frac{800}{(x-5)}$ day

Route C , which is 100 km longer than route A , has easier condition and would expect to cover (x+5) km per day.

Time =$\frac{900}{(x+5)}$ day

Given, route C takes 20 days less than route B .

Therefore,

$\frac{800}{(x-5)}-\frac{900}{(x+5)}=20$

$\Rightarrow \frac{800(x+5)-900(x-5)}{(x-5)(x+5)} =20$

$\Rightarrow 20(x^2-25)=-100x+8500$

$\Rightarrow (x^2-25)=-5x+425$

⇒x²+5x-450=0

⇒x=18.86

Therefore $\frac{800}{18.86} =42.41$ days that he expects to take on route A.