To determine the distance traveled in five seconds using the expression \(50T\), we first need to establish the meaning of \(T\). According to the information provided, \(50T\) gives the distance in feet traveled in two seconds. We can interpret this as:
\[ \text{Distance in 2 seconds} = 50T \]
Next, we need to evaluate the expression with the value provided. You stated \(50T - 40 = 5\) seconds. This suggests that at \(T\) indicates a function of \(time\) and \(40\) is possibly an offset or adjustment.
The next step is to determine the value of \(T\) at \(5\) seconds compared to the original \(2\) seconds. Since \(T\) is the time parameter, we can also note:
Given that distance is proportional to time, we can find the distance for \(5\) seconds using a scaled relation. Let's interpret \(50T\) in a general sense, specifically as the distance formula based on time directly analogous to speed.
Given that:
\[ \text{Distance for 2 seconds} = 50T \text{ (where T is time in seconds)} \]
Now that we need to find the distance traveled in \(5\) seconds, we can consider the ratio of times:
\[ \text{Distance for 5 seconds} = \left( \frac{5}{2} \right) \times \text{Distance for 2 seconds} \]
Substituting the expression for distance in \(2\) seconds:
\[ \text{Distance for 5 seconds} = \left( \frac{5}{2} \right) \times (50T) = \left( \frac{5 \times 50T}{2} \right) = 125T \]
Thus, the distance traveled in \(5\) seconds is \(125T\).
Since you've stated \(50T - 40\) equals \(5\) seconds, to clarify \(T\), we can solve:
- Let \(T\) be \(1\) second based on the earlier equation since we're converting from distance/time aggregate:
So, let’s put:
\[ 50T - 40 = 5 \implies 50T = 45 \implies T = \frac{45}{50} = 0.9\text{ (2 seconds)} \]
Hence recalculating \(T\) for \(5\):
\[ \text{Distance for 5 seconds} = 125 \times 0.9 = 112.5 \text{ feet} \]
Thus, the distance traveled in five seconds is 112.5 feet.
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