The formula for the distance traveled over time [tex][tex]$t$[/tex][/tex] and at an average speed [tex][tex]$v$[/tex][/tex] is [tex][tex]$v \cdot t$[/tex][/tex].

Amit ran for 40 minutes at a speed of about 5 kilometers per hour. What calculation will give us the estimated distance Amit ran in kilometers?

Choose 1 answer:
(A) [tex][tex]$5 \cdot 40 \cdot 60$[/tex][/tex]
(B) [tex][tex]$5 \cdot 1000 \cdot 40$[/tex][/tex]
(C) [tex][tex]$5 \cdot \frac{40}{60}$[/tex][/tex]
(D) [tex][tex]$\frac{5}{1000} \cdot 40$[/tex][/tex]



Answer :

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]