# A motorboat can go 8 miles downstream on a river in 20 minutes. it takes 30 minutes for the boat to go upstream the same

###### Question:

## Answers

2. x + y = 82

x - y = 24

add

2x = 106

x = 53

x + y = 82

53 + y = 82

y = 82 - 53

y = 29

solution is : (53,29)

3. y = 2x

y = 4x + 6

2x = 4x + 6

2x - 4x = 6

-2x = 6

x = -3

y = 2x

y = 2(-3)

y = -6

solution is (-3,-6)

4. 5x + 8y = -29

7x - 2y = -67...multiply by 4

5x + 8y = -29

28x - 8y = - 268 ..result of multiplying by 4

add

33x = - 297

x = - 9

5x + 8y = -29

5(-9) + 8y = -29

-45 + 8y = -29

8y = -29 + 45

8y = 16

y = 2

solution is : (-9,2)

5. y = -4x + 6

y = -5x - 4

-4x + 6 = -5x - 4

-4x + 5x = -4 - 6

x = -10

y = -4x + 6

y = -4(-10) + 6

y = 40 + 6

y = 46

solution is (-10,46)

6. H(m) = 2m + 12

H(m) = 3m + 10

7. -8x + 4y > -52

4y > 8x - 52

y > 2x - 13 <==

8. 3x - y = 28

3x + y = 14

add

6x = 42

x = 7

3x - y = 28

3(7) - y = 28

21 - y = 28

-y = 28 - 21

-y = 7

y = -7

solution is (7,-7)

10. 5x - 5y > 70

-5y > -5x + 70

y < x - 14 <==

11. sorry...dont know

12. y = 4x + 4

y = -3x - 3

4x + 4 = -3x - 3

4x + 3x = -3 - 4

7x = -7

x = -1

y = 4x + 4

y = 4(-1) + 4

y = 0

solution is (-1,0)

13. -12x - 2y > - 42

-2y > 12x - 42

y < -6x + 21 <==

14. -5x + 2y = 9

3x + 5y = 7

solution is (-1,2)

15. 3x + 6y = -2

15x + 30y = -10divide by 5 to reduce = 3x + 6y = -2

is the same lineinfinite solutions

1. (the graph)y < = 3x - 43rd one

9. (2nd graph)y < = -3x + 4last one

A. 4 mph

Step-by-step explanation:

For this multiple-choice question, the only reasonable answer is the correct one. The upstream speed is (8 mi)/(1/2 h) = 16 mph, so the speed of the current must be less than that.

The only answer choice less than 16 mph is 4 mph, the correct current speed.

Downstream speed is (8 mi)/(1/3 h) = 24 mph. The speed of the current adds to the speed of the boat to give the downstream speed, and it subtracts from the speed of the boat to give the upstream speed. Then the current speed is half the difference of the travel speeds, (24 -16) mph/2 = 4 mph.

4 miles per hour is the answer

4 mph

Step-by-step explanation:

Let x is the speed of the current

Let y is the speed of the motorboat

As we know: speed = distance / time

It takes 30 minutes (= 1/2 hours) for the boat to go upstream the same 8 miles

y - x = 8 / [tex]\frac{1}{2}[/tex] mph

<=> y - x = 16 mph (1)

<=> x = y -16 mph

A motorboat can go 8 miles downstream on a river in 20 minutes (= 1/3 hour)

y + x = 8 / [tex]\frac{1}{3}[/tex] mph

<=> y + x = 24 mph (2)

Solve the system of equation (1) and (2), we have:

y + x = 24 mph

<=> y + y -16 = 24 mph

<=> 2y = 40 mph

<=> y = 20 mph

=> x = 20 -16 = 4 mph

So the speed of the current is 4 mph

4 mph

Step-by-step explanation:

Let's say m is the speed of the motor boat, and r is the speed of the river.

20 minutes is 1/3 hour, and 30 minutes is 1/2 hour.

Distance = rate × time

8 = (m + r) × 1/3

8 = (m − r) × 1/2

We want to find the value of r. Let's start by solving for m in one equation, then substitute into the other.

8 = (m − r) × 1/2

16 = m − r

m = r + 16

8 = (m + r) × 1/3

8 = (r + 16 + r) × 1/3

8 = (2r + 16) × 1/3

24 = 2r + 16

8 = 2r

r = 4

The speed of the river's current is 4 miles per hour.

The speed of the current is 4 miles/hour

Step-by-step explanation:

Let us assume that,

x = speed of the boat,

y = speed of the current.

We know that,

[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

A motorboat can go 8 miles downstream on a river in 20 minutes or [tex]\dfrac{20}{60}[/tex] hours.

[tex]\Rightarrow x+y=\dfrac{8}{\frac{20}{60}}=\dfrac{8\times 60}{20}[/tex]

[tex]\Rightarrow x+y=24[/tex] --------------------------1

It takes 30 minutes for the boat to go upstream the same 8 miles.

[tex]\Rightarrow x-y=\dfrac{8}{\frac{30}{60}}=\dfrac{8\times 60}{30}[/tex]

[tex]\Rightarrow x-y=16[/tex] ----------------------------2

Subtracting equation 1 and 2,

[tex]\Rightarrow x+y-x+y=24-16[/tex]

[tex]\Rightarrow 2y=8[/tex]

[tex]\Rightarrow y=4[/tex] miles/hour

Downstream it's 24 miles per hour and upstream it's 16 miles per hour

the correct answer is C = 4 mph