(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.
