Question

A boat travels 12 km downstream and 6 km upstream in 3 hours. The same boat takes fifty percent extra time to cover 10 km  downstream and 16 km upstream. If the same boat travels 20 km downstream and z km upstream in 4 hours find z. 9km 7.5km 8km 4.5km​

Answer 1

Answer:

this is the answer

Step-by-step explanation:

please mark me as brainliest

Answer 2

The value of z is 4.5 and option  d is correct.

Step-by-step explanation:

Given:

3 hours time is taken by boat  for travelling 12 km downstream and 6 km upstream.

Fifty percent extra time is taken by boat  for travelling 10 km downstream and 16 km upstream.

4 hours time is taken by boat  for 20 km downstream and z km upstream

To Find:

The value of z .

Formula Use:

Upstream  speed of boat  = (p−q) km/hr, where  p is the speed of the boat in still water and q is the speed of the stream .

Downstream speed of boat  = (p+q)Km/hr, where  p is the speed of the boat in still water and  q is the speed of the stream.      

Time =  distance /speed  

Solution:

As given- 3 hours time is taken by boat  for travelling 12 km downstream and 6 km upstream.

$\frac{12}{p+q} +\frac{6}{p-q} =3$                  ------------ equation no .01

As given- Fifty percent extra time is taken by boat  for travelling 10 km downstream and 16 km upstream.

That means  4.5 hours is taken by boat  for travelling 10 km downstream and 16 km upstream.

$\frac{10}{p+q} +\frac{16}{p-q} =4.5$                           ------------ equation no.02

Dividing equation no. 01 by 3 and multiplying by 8.

Then   $\frac{32}{p+q} +\frac{16}{p-q} = 8$                 ------------- equation no.03

Subtracting  equation no. 02 by equation no.03.

Then $p+q=6.285$     --------------- equation no. 04.

Putting value of p+q in equation no. 02.

Then  $\frac{10}{6.285} +\frac{16}{p-q} =4.5$

         $\ 1.591 +\frac{16}{p-q} =4.5$

                      $\frac{16}{p-q} =2.909$

                    $p-q=5.5$     ------------- equation no. 05.

As given-4 hours time is taken by boat  for 20 km downstream and z km upstream

$\frac{20}{p+q} +\frac{z}{p-q} =4$

Putting the value of p+q and p-q from equation no.04 and equation 05.

Then $\frac{20}{6.285} +\frac{z}{5.5} =4.5$

        $\ 3.182+\frac{z}{5.5} =4.5$

        $\frac{z}{5.5} =0.818$

           $z=4.499$

           $z \approx4.5$

           

Thus,The value of z is 4.5 and option  d is correct.

Correct Question

A boat travels 12 km downstream and 6 km upstream in 3 hours. The same boat takes fifty percent extra time to cover 10 km  downstream and 16 km upstream. If the same boat travels 20 km downstream and z km upstream in 4 hours find z.

Options.

a. 9km

b..5km

c.8km

d.4.5km