3. The formula d = rt relates distance, rate, and time. If a given distance is tripled and its corresponding time remains the same, which of the following is equivalent to the new rate?
Answer: B
The new rate is equivalent to (3d)/t.
When the distance is tripled while keeping the time constant, the new rate can be expressed as the new distance divided by the same time, resulting in (3d)/t.
A) 3dt
This option suggests multiplying the original distance by 3 and the time, which does not accurately reflect the rate calculation. Rate is defined as distance divided by time, not a product of distance and time.
B) (3d)/t
This option correctly represents the new rate since it takes the tripled distance (3d) and divides it by the unchanged time (t). This aligns with the formula for rate, r = d/t, confirming its validity.
C) t/(3d)
This option incorrectly reverses the relationship by placing time in the numerator and tripled distance in the denominator. The rate should be a function of distance divided by time, not the inverse.
D) d/(3t)
While this option maintains the format of distance over time, it incorrectly reduces the time instead of increasing the distance. The rate should reflect the increase in distance, not a decrease in time.
Conclusion
The correct answer, (3d)/t, accurately reflects the relationship defined by the formula d = rt after tripling the distance while keeping time constant. The other options fail to properly apply the rate formula, either by altering the components incorrectly or misrepresenting the relationship between distance and time. Thus, option B is definitively the right choice.