Question

A rescue boat takes 12 hours to row 90 km downstream and 70 km upstream. what is the rate of current if the boat take 9 hours to row 72 km downstream

Answer 1

The question is incomplete

Complete question as below:

A rescue boat takes 12 hours to row 90 km downstream and 70 km upstream. what is the rate of current if the boat take 9 hours to row 50 km upstream and 72 km downstream?

Answer:

4 km/h

Step-by-step explanation:

Define x and y:

Let x be the speed upstream

Let y be the speed downstream

The boat takes 12 hours to row 90 km downstream and 70 km upstream

90/y + 70/x = 12

The boat takes 9 hours to row 50 km upstream and 72 km downstream

72/y + 50/x = 9

90/y + 70/x = 12 ---------- [ 1 ]

72/y + 50/x = 9  ---------- [ 2 ]

From [ 1 ]:

90/y + 70/x = 12

90x + 70y = 12xy

45x + 35y = 6xy

35y = 6xy - 45x

35y = x(6y - 45)

x = 35y/(6y - 45) ----------  sub into [ 2 ]

72/y + 50/x = 9

72/y + (50 ÷ 35y/(6y - 45) ) = 9

72/y + 50(6y - 45)/35y = 9

72(35) + 50(6y - 45) = 9(35y)

2520  + 300y - 2250 = 315y

315y - 300y = 2520 - 2250

15y = 270

y = 18

Sub y = 18 into equation [ 1 ]:

90/y + 70/x = 12

90/18 + 70/x = 12

5 + 70/x = 12

70/x = 7

7x = 70

x = 10

Find the speed:

Upstream = x = 10 km/h

Downstream = y = 18 km/h

Find the rate of the current:

Speed of the current = 1/2 (downstream - upstream)

Speed of the current = 1/2 (18 - 10) = 4 km/h

Answer: The rate of the current is 4 km/h

Answer 2

We will assume the speed of the boat as B and the Speed of current as C

speed of downstream = (B + C) Km/h

speed of upstream = (B - C) Km/h

We are given,

time = distance /speed

so, time taken in downstream + time taken in upstream = 12 h

90/(B + C) + 70/(B - C) = 12 ----(1)

Time taken in downstream = 9 h

72/(B + C) = 9

B + C = 8 km/h---------(2) , put it in equation (1)

90/8 + 70/(B -C) = 12

45/4 + 70/(B - C) = 12

70/(B - C) = 12 - 45/4 = 3/4

B - C = 280/3 km/h -------(3)

Now we will solve both equations (2) and (3),

2B = 280/3 + 8 => B = 140/3 + 4 = 152/3 km/h

now we will Put B in equation (2) ,

C = 8 - 152/3 = (24-152)/3 = -128/3 km/h

here , negative sign shows that Current is just opposite side of our assumption

So speed of current = -128/3 km/h