Question

Sun, a kayaker, paddles 8 miles upstream (against the current) in 2 hours. Returning to her original location, she paddles downstream (with the current) the same distance in 1 hour. The equations represent x, the paddling speed, and y, the speed of the current.2(x – y) = a
b(x + y) = 8

Which are true? Check all that apply.

a = 8


b = 8


a = 1


b = 1


a = b

Answer 1

Answer:

a=8 and b=1

Step-by-step explanation:

Given : Sun, a kayaker, paddles 8 miles upstream (against the current) in 2 hours. Returning to her original location, she paddles downstream (with the current) the same distance in 1 hour. The equations represent x, the paddling speed, and y, the speed of the current.

$2(x - y) = a$ and $b(x + y) = 8$

To find : Which are true?

Solution :

If x represents the paddling speed, and y represents the speed of the current.

The relative speed in upstream is x-y

Relative time in downstream= x+y

A kayaker, paddles 8 miles upstream (against the current) in 2 hours.

$\text{Distance}=\text{Speed} \times \text{Time}$

$8=(x-y)\times 2$

Comparing with $2(x - y) = a$

We get, a=8

Returning to her original location, she paddles downstream (with the current) the same distance in 1 hour.

$\text{Distance}=\text{Speed} \times \text{Time}$

$8=(x+y)\times 1$

Comparing with $b(x + y) = 8$

We get, b=1

Thus, a=8 and b=1

Therefore, Option 1 and 4 is correct.

Answer 2

Answer: a=8 and b=1

Step-by-step explanation:

If x represents the paddling speed, and y represents the speed of the current.

Then Relative speed in upstream =x-y

Relative time in downstream=x-y

When she paddles upstream then distance covered by her=$speed\times\ time$

⇒8=(x-y)2 or 2(x-y)=8

Thus we get, a=1

When she paddles downstream then distance covered by her=$speed\times\ time$

⇒8=(x+y)1 or 1(x+y)=8

Thus we get b=1