If a boatman rows his boat 35km up stream and 55km downstream in 12 hours and he can row 30km upstream and 44 km downstream in 10hr , then the speed of the stream and that of the boat in still water

To solve this problem, let us assume linear motion so that we can use the equation:

t = d / v

where t is time, d is distance and v is velocity

First let us assign some variables, let us say that the velocity upstream is Vu while Velocity downstream is Vd, so that:

35 / Vu + 55 / Vd = 12                     ---> 1

30 / Vu + 44 / Vd = 10                     ---> 2

We rewrite equation 1 in terms of Vu:

(35 / Vu + 55 / Vd = 12) Vu

35 + 55 Vu / Vd = 12 Vu

12 Vu – 55 Vu / Vd = 35

Vu (12 – 55 / Vd) = 35

Vu = 35 / (12 – 55 / Vd)                  ---> 3

Also rewriting equation 2 to in terms of Vu:

Vu = 30 / (10 – 44 / Vd)                  ---> 4

Equating 3 and 4:

35 / (12 – 55 / Vd) = 30 / (10 – 44 / Vd)   

35 (10 – 44 / Vd) = 30 (12 – 55 / Vd)

Multiply both sides by Vd:

350 Vd – 1540 = 360 Vd – 1650

10 Vd = 110

Vd = 11 km / h

Using equation 3 to solve for Vu:

Vu = 35 / (12 – 55 / 11)

Vu = 5 km / h

Answers:

Vu = 5 km / h = velocity upstream

Vd = 11 km / h = velocity downstream

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you

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