A car travels at a constant speed of r miles per hour. If the car travels 240 miles in 4 h… — ACT

A car travels at a constant speed of $r$ miles per hour. If the car travels $240$ miles in $4$ hours, which of the following equations can be used to determine the value of $r$ ?

$4r = 240$ Answer
B
$r + 4 = 240$
C
$\frac{r}{4} = 240$
D
$r - 4 = 240$
E
$240r = 4$

Answer

The equation

4r = 240

represents the relationship because distance equals rate multiplied by time.

The relationship between distance, rate, and time is given by the formula

\text{Distance} = \text{Rate} \times \text{Time}

. Substituting the distance of

240

miles and the time of

4

hours into this formula yields

240 = r \times 4

, which is equivalent to

4r = 240

Step-by-Step Solution

Identify the formula relating distance, rate, and time.

\text{Distance} = \text{Rate} \times \text{Time}

(or

d = r \cdot t

)

This is the standard physical relationship governing constant speed motion.

Substitute the given values into the formula.

240 = r \cdot 4

The total distance

d

is given as

240

miles, the time

t

4

hours, and the speed is the variable

r

Rewrite the equation in standard algebraic format.

4r = 240

Multiplying the variable

r

by the coefficient

4

is conventionally written with the number first.

Key Concept

Translating a constant rate word problem into a one-step linear equation.

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Answer

Step-by-Step Solution

Key Concept

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