A ferry takes a total of 22 hours to cover 240 km downstream and 280 km upstream. The downstream speed of the ferry is 10 km/hr more than its upstream speed. Find the time taken by the ferry to cover 450 km downstream.

The correct option is 15 hours.

Given Data:
Total time taken = 22 hours
Distance covered downstream = 240 km
Distance covered upstream = 280 km
Downstream speed is 10 km/hr more than the upstream speed.

Step 1: Define variables for speed
Let the upstream speed of the ferry be $u$ km/hr.
Since downstream speed is 10 km/hr more than upstream speed, downstream speed ($d$) is:
$d=u+10$ km/hr.

Step 2: Formulate the time equation
We know that:
$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$
Time taken to cover 240 km downstream:
${\text{Time}}_{\text{downstream}}=\frac{240}{u+10}$
Time taken to cover 280 km upstream:
${\text{Time}}_{\text{upstream}}=\frac{280}{u}$

The total time given is 22 hours:
$\frac{240}{u+10}+\frac{280}{u}=22$

Step 3: Solve for upstream speed ($u$)
Divide the entire equation by 2:
$\frac{120}{u+10}+\frac{140}{u}=11$

Combine terms over a common denominator:
$\frac{120u+140(u+10)}{u(u+10)}=11$
$120u+140u+1400=11u(u+10)$
$260u+1400=11u^2+110u$
$11u^2-150u-1400=0$

Factorize the quadratic equation:
$11u^2-220u+70u-1400=0$
$11u(u-20)+70(u-20)=0$
$(11u+70)(u-20)=0$

Since speed cannot be negative:
$u=20$ km/hr.

Step 4: Calculate downstream speed
Downstream speed ($d$):
$d=u+10=20+10=30$ km/hr.

Step 5: Find time taken to cover 450 km downstream
$\text{Time}=\frac{450}{30}=15$ hours.

Therefore, the ferry takes 15 hours to cover 450 km downstream.