The distance formula can be written as d=rt
, where d=
distance traveled, r=
the rate of speed, and t=
the length of time traveled. Johan travels 35 miles by bicycle in 1.75 hours. What is Johan’s rate of speed in miles per hour? Explain the solution to the real-world problem.(1 point)
Responses
Johan travels at a rate of 20 miles per hour.
Johan travels at a rate of 20 miles per hour.
Johan travels at a rate of 10 miles per hour.
Johan travels at a rate of 10 miles per hour.
Johan travels at a rate of 61.25 miles per hour.
Johan travels at a rate of 61.25 miles per hour.
Johan travels at a rate of 2 miles per hour.
To find Johan's rate of speed in miles per hour, we can use the distance formula d = rt. Given that Johan travels 35 miles in 1.75 hours, we need to solve for r (rate of speed).
We can rearrange the formula to solve for r: r = d / t.
Plugging in the values, we get r = 35 miles / 1.75 hours.
Using a calculator, we find that r ≈ 20 miles per hour.
Therefore, Johan's rate of speed is approximately 20 miles per hour.
Raji draws a square with a side length of x+5
cm. Ava draws a regular hexagon with a side length of x−1
cm. The two figures have the same perimeter. Write an equation that allows you to solve for x
. What is the value of x
?(1 point)
Responses
12
12
18
18
13
13
26
26
To find the equation that allows us to solve for x and the value of x, we need to consider the perimeters of the square and the regular hexagon.
The perimeter of a square is given by P = 4s, where s is the side length of the square.
The perimeter of a regular hexagon is given by P = 6s, where s is the side length of the hexagon.
In this problem, Raji draws a square with a side length of x+5 cm, so the perimeter of the square is 4(x+5) cm.
Ava draws a regular hexagon with a side length of x-1 cm, so the perimeter of the hexagon is 6(x-1) cm.
Since the two figures have the same perimeter, we can set the two expressions equal to each other:
4(x+5) = 6(x-1)
Now we can solve for x by simplifying and isolating the variable:
4x + 20 = 6x - 6
20 + 6 = 6x - 4x
26 = 2x
x = 26/2
x = 13
Therefore, the equation that allows us to solve for x is 4(x+5) = 6(x-1), and the value of x is 13.
To find Johan's rate of speed in miles per hour, we can use the formula d=rt, where d is the distance traveled, r is the rate of speed, and t is the length of time traveled.
In this case, Johan traveled a distance of 35 miles in 1.75 hours. We can plug these values into the formula:
35 = r * 1.75
To solve for r, we divide both sides of the equation by 1.75:
35/1.75 = r
The result is r = 20.
Therefore, Johan's rate of speed is 20 miles per hour.