Question

Motarboat takes 6 hrs. to cover 100km downstream and 30km uostream . if the motorboat goes 75km downstream and returnbacks to it's starting point in 8 hours , find the speed of the motorboat in still water and the rate of stream .

Answer 1

solution

Let the speed of the motor boat in still water be x km/h.

Let the rate of flow of the stream be y km/h

Speed of boat upstream = (x - y) km/h.

Speed of boat downstream = (x + y)km/h.

we know time = distance/speed.

now , A to Q,

Time for 100 km downstream and 30 km upstream

100/(x + y) + 30/(x - y)

And it takes 6 hrs to cover downstream and upstream. Then

100/(x + y) + 30/(x - y) = 6

Time for 75 km downstream and returning (means 75 km upstream)

= 75/(x + y) + 75/(x - y)

Given that the time taken is 8 hours

75/(x + y) + 75/(x - y) = 8

now the equation should be .

100p + 30q = 6

50p + 15q = 3------------( 1 )

75p + 75q = 8----------( 2 )

from--------( 1 ) &---------( 2 )

multiply by ( 3 ) in -----( 1 )

250p + 75q = 15

75p + 75q = 8

(–)______(–)____(–)

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

175p = 7

p = 1/25 [ put in -------( 1 ) ]

50(1/25) + 15q = 3

2 + 15q = 3

q = 1/15 = 1/(x - y)

x - y = 15------------( 3 )

p = 1/25 = 1/(x + y)

x + y = 25---------( 4 )

From---------( 3 ) &----------( 4 )

x - y = 15

x + y = 25

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

2x = 40

x = 20 [ put in ------( 3 ) ]

x - y = 15

20 - y = 15

y = 20 - 15

y = 5 , x = 20

Hence, the speed of the motor boat in still water is 20 km/h and rate of flow of the stream is 5 km/h.

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Answer 2

Answer:

Step-by-step explanation:

Speed of stream be x

Speed of motorboat in still water be y

100/(x+y) + 30/(x-y) = 6 --------- (1)

75/(x+y) + 75/(x-y) = 8 ---------------(2)

Multiply equation (1) by 2.5

250/(x+y) + 75/(x-y) = 15 -------------(3)

(3) - (2)

175/(x+y) = 7

x+y = 25 -------------------------------(4)

Multiply equation (1) by 3 and (2) by 4

300/(x+y) + 90/(x-y) = 18 --------- (5)

300/(x+y) + 300/(x-y) = 32 ---------------(6)

(6) - (5)

210/(x-y) = 14

x-y = 15 ---------------------(7)

(4) + (7)

2x= 40

x = 20

Put x=20 in (7)

20-y = 15

y = 5