The formula for the distance traveled over time $t$ and at an average speed $v$ is $v \cdot t$ . 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: $\newline$ (A) $5 \cdot 40 \cdot 60$ $\newline$ (B) $5 \cdot 1000 \cdot 40$ $\newline$ (C) $5 \cdot \left(\frac{40}{60}\right)$ $\newline$ (D) $\left(\frac{5}{1000}\right) \cdot 40$

Full solution

Q. The formula for the distance traveled over time

t

and at an average speed

v

v \cdot t

. 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:

\newline

(A)

5 \cdot 40 \cdot 60

\newline

(B)

5 \cdot 1000 \cdot 40

\newline

(C)

5 \cdot \left(\frac{40}{60}\right)

\newline

(D)

\left(\frac{5}{1000}\right) \cdot 40

Understand the formula: Understand the formula for distance. $\newline$ The formula for distance is $\text{distance} = \text{speed} \times \text{time}$ . Amit's speed is given in kilometers per hour, and his running time is given in minutes. We need to make sure the units are consistent before we calculate the distance.
Convert running time: Convert Amit's running time from minutes to hours. $\newline$ Since there are $60$ minutes in an hour, we divide the number of minutes Amit ran by $60$ to convert his running time to hours. $\newline$ $40$ minutes $\div$ $60$ minutes/hour = $\frac{40}{60}$ hours
Calculate distance: Calculate the distance using the formula. $\newline$ Now we can use the formula $\text{distance} = \text{speed} \times \text{time}$ with the time in hours. $\newline$ $\text{Distance} = 5 \, \text{km/hour} \times \left(\frac{40}{60}\right) \, \text{hours}$
Perform multiplication: Perform the multiplication to find the distance. $\newline$ Distance = $5 \times (40/60)$ $\newline$ Distance = $5 \times (2/3)$ (since $40/60$ simplifies to $2/3$ ) $\newline$ Distance = $(5 \times 2)/3$ $\newline$ Distance = $10/3$ $\newline$ Distance = $3.333\ldots$ kilometers
Match with choices: Match the calculation with the given choices. $\newline$ The calculation we performed, $5 \times (40/60)$ , matches choice (C).