Question

a boat goes 12 km upstream and 40km downstream in 8 hours.it can go 16km upstream and 32 km downstream in the same time. find the speed of the boat in still water and the speed of the stream

Answer 1

hope it helps u a lot

Answer 2

The speed of the boat in still water = 6 km/hr

The speed of the stream = 2 km/hr

Step-by-step explanation:

We are given that a boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time.

Let the speed of the boat in still water be x km/hr

and the speed of the stream be y km/hr.

Now, as we know that;

Speed of upstream is represented as = (x - y) km/hr

Speed of downstream is represented as = (x + y) km/hr

Also, according to the Distance-Speed-Time formula;

                            Time  =  $\frac{\text{Distance}}{\text{Speed}}$

So, according to the question;

• The first condition states that a boat goes 12 km upstream and 40km downstream in 8 hours, that means;

                        $\frac{12}{x-y}+\frac{40}{x+y} = 8 \text{ hours}$  ----------- [Equation 1]

• The second condition states that a boat can go 16km upstream and 32 km downstream in the same time, that means;

                        $\frac{16}{x-y}+\frac{32}{x+y} = 8 \text{ hours}$  ----------- [Equation 2]

Now, substitute ( $\frac{1}{x-y} = a$ ) and ( $\frac{1}{x+y}=b$ ) in equation 1 and 2, i.e;

                       12a + 40b = 8   -------- [equation 3]

                       16a + 32b = 8  ---------- [equation 4]

Using equation 3, we get;

                        12a = 8 - 40b

                          a  =  $\frac{8-40b}{12}$

                          a  =  $\frac{2-10b}{3}$

Putting value of a in equation 4 we get;

                      16a + 32b = 8

                      $16(\frac{2-10b}{3}) +32b=8$

                       $\frac{32-160b+96b}{3}=8$

                        ${32-64b}}=24$

                          b  =  $\frac{8}{64 } = \frac{1}{8}$

So, a  =  $\frac{2-10b}{3}$  =  $\frac{2-10(\frac{1}{8} )}{3}$

          =  $\frac{6}{24} =\frac{1}{4}$

Now, putting values of a and b in the original expression we get;

 $a = \frac{1}{x-y} = \frac{1}{4}$                              $b= \frac{1}{x+y} = \frac{1}{8}$

    x - y = 4                                      x + y = 8

Using elimination method in both above equations, we get;

                 x = 6 km/hr      and      y = 2 km/hr

This means speed of the boat in still water = x = 6 km/hr

and speed of the stream = y = 2 km/hr.