1 cm represents 2 km; is not correct because this is actually the smallest of the scales presented, meaning that 1 cm on the map is equal to 200,000 cm on the ground.

1 : 50,000; is not correct because this is the second-largest scale from the options.

1 : 25,000; is correct because it is the largest scale, with 1 cm on the map representing 25,000 cm on the ground. The smaller the scale, the larger it is.

1 : 100,000; is not correct because it is the third-largest, with 1 cm on the map representing 100,000 cm on the ground.

6 0

3 years ago

ALGEBRA:Chase rides his bike 5 miles to school in 25 minutes. The relationship between the distance he rides and the time it tak

bezimeni [28]

(D) Distance traveled by Chase on bike = 5 miles

(T) Time taken by Chase to travel that distance = 25 minutes

D and T are directly related.

Part A (Equation)

Since, D and T are directly related,

⇒ D ∝ T (i.e. D is directly proportion to T)

⇒ D = k × T (using k as constant variation, as suggested in the question)

So the equation that represents the relation between T and D is D = k × T.

Part B (Value and units for k)

When we put the values of T and D in the equation D = k × T, we get:

5 = k × 25

Solving the above equation and moving 25 to the Left Hand Side (LHS) of the equation

⇒ 5 ÷ 25 = k

⇒ 0.2 = k OR

⇒ k = 0.2

Hence, value of k is 0.2. This is the rate at which Chase drove his bike to school.

Now, to determine the unit of k we will simply put the units of D and T in the equation.

⇒ 5 miles = k × 25 minutes

⇒ 0.2 miles/minute = k OR

⇒ k = 0.2 miles/minute

Hence, the unit for k is miles/minute or miles per minute.

Part C (Time taken to ride 8 miles)

Now, if Chase drives his bike at the same rate every day, i.e. at 0.2 miles/minute, then we need to determine how much time he takes to ride 8 miles. Putting the values of k and D in the equation:

⇒ 8 = 0.2 × T

⇒ T = 40 minutes

So, Chase would take 40 minutes to cover a distance of 8 miles.

7 0

3 years ago