To determine the distance Amit ran in kilometers, we need to follow these steps:
1. Convert the time from minutes to hours:
Given that Amit ran for 40 minutes, we need to convert this time into hours since the speed is given in kilometers per hour (km/h).
[tex]\[
\text{Time in hours} = \frac{40 \, \text{minutes}}{60 \, \text{minutes per hour}} = \frac{40}{60} \, \text{hours}
\][/tex]
2. Calculate the distance:
Using the formula for distance [tex]\( \text{Distance} = \text{Speed} \times \text{Time} \)[/tex], we can plug in the values.
The speed [tex]\( v \)[/tex] is 5 kilometers per hour (km/h), and the time [tex]\( t \)[/tex] in hours is [tex]\(\frac{40}{60}\)[/tex].
3. Perform the multiplication:
[tex]\[
\text{Distance} = 5 \, \text{km/h} \times \frac{40}{60} \, \text{hours}
\][/tex]
From the options provided, we see that:
(A) [tex]\( 5 \cdot 40 \cdot 60 \)[/tex]: This calculation mistakenly involves multiplication by 60 instead of dividing by 60, which is incorrect.
(B) [tex]\( 5 \cdot 1000 \cdot 40 \)[/tex]: This calculation incorporates an extraneous multiplication by 1000, which is incorrect.
(C) [tex]\( 5 \cdot \frac{40}{60} \)[/tex]: This correctly follows our step-by-step solution of multiplying the speed by the correctly converted time in hours.
(D) [tex]\( \frac{5}{1000} \cdot 40 \)[/tex]: This calculation incorrectly involves dividing the speed by 1000, which is incorrect.
Hence, the correct calculation that will give us the estimated distance Amit ran in kilometers is:
[tex]\[
\boxed{5 \cdot \frac{40}{60}}
\][/tex]
