Question

A boat goes 36 km upstream &35 km downstream in 11hrs.again in 11hrs it can go 45km upstream and 39km downstream.the speed of the boat in still water and the speed of stream in kmper hrs

Answer 1

Answer:

Step-by-step explanation:

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

Let the speed of stream be y km/hr

In up-stream, speed = (x - y) km/hr

In down-stream, speed = (x + y) km/hr

Also, speed, distance and time are related as below

Distance = Speed × Time

Given that boat goes 36 km upstream and 35 km downstream in 11 hours.

Time taken is calculated as

36/(x - y) + 35/(x + y) = 11------- (1)

Also, given that boat goes 45 km upstream and 39 km downstream in 11 hours

Thus, we get

45/(x - y) + 39/(x + y) = 11 ----- (2)

Let 1/(x - y) = u and 1/(x + y) = v

Substituting the values of u and v in (1) and (2), we get

36u + 35v = 11 ---- (3)

45u + 39v = 11 ---- (4)

Solving the above two equations

 36u + 35v = 11 × 5

 45u + 39v = 11 × 4

------------------------------

 180u + 175v = 55

 180u + 156v = 44

(-)        (-)          (-)

------------------------------

  0u + 19v = 11

   v = 11/19

Substituting the value of v in (3), we get

36u +35 × 11/19 = 11

36u = 11 - 385/19

36u = (209 - 385)/19

u = - 176/(19 × 36)

u = -44/171

Now, we have

1/(x - y) = -44/171

x - y = -171/44

44x - 44y = -171 ----- (5)

Also,

1/(x + y) = 11/19

x + y = 19/11

11x + 11y = 19 --------- (6)

Now, again solving (5) and (6), we get

44x - 44y = -171 ×  1

11x + 11y = 19      ×  4

---------------------------------

 44x - 44y = -171

 44x + 44y = 76

(-)      (-)         (-)

---------------------------

 0x - 88y = - 247

       88y = 247

        y = 247/88

 

Also, putting the value of y in (6)

11x + 11 × 247/88 = 19

11x + 247/8 = 19

11x = 19 - 247/8

11x = 152 - 247/8

x = - 95/88

Question is incorrect, as in 11 hours - it is going 36km up stream and 35 km downstream

Again in same 11 hours, boat is going 45km upstream and 39 km downstream.

Distance going in upstream and downstream is increasing in second case, but time is not increasing.

Either the time should increase, or the distance traveled in up-stream and downstream will decrease