The total time taken by a boat to cover 400 km downstream and 320 upstream is 40 hours. If downstream speed of the boat is 4 km/hr more than upstream speed of the boat, then find the time taken (in hours) by the boat to cover 720 km downstream.

The correct answer is 36.

Step-by-step derivation:

Let the upstream speed of the boat be $u$ km/hr.
According to the problem, the downstream speed of the boat is 4 km/hr more than its upstream speed.
Therefore, the downstream speed of the boat, $d$, is:
$d=u+4$

We are given that the total time taken to cover 400 km downstream and 320 km upstream is 40 hours.
Using the formula $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$, we can write the equation as:
$\frac{400}{d}+\frac{320}{u}=40$

Substitute $d=u+4$ into the equation:
$\frac{400}{u+4}+\frac{320}{u}=40$

Divide the entire equation by 40 to simplify:
$\frac{10}{u+4}+\frac{8}{u}=1$

Now, find a common denominator and solve for $u$:
$\frac{10u+8(u+4)}{u(u+4)}=1$
$10u+8u+32=u^2+4u$
$18u+32=u^2+4u$
$u^2-14u-32=0$

Factor the quadratic equation:
$u^2-16u+2u-32=0$
$u(u-16)+2(u-16)=0$
$(u-16)(u+2)=0$

Since speed cannot be negative, we discard $u=-2$.
Thus, the upstream speed is:
$u=16$ km/hr

The downstream speed is:
$d=u+4=16+4=20$ km/hr

Now, find the time taken by the boat to cover 720 km downstream:
$\text{Time}=\frac{\text{Distance}}{\text{Downstream Speed}}=\frac{720}{20}=36$ hours.