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x=78(7.7-t)
Priya is traveling by train for her job. The equation gives her distance from her destination,
x, after
t hours. How long will it take for Priya to reach her destination?
Choose 1 answer:
(A) 7.7 hours
(B) 10.1 hours
(c) 78.0 hours
(D) 600.6 hours

$x=78(7.7-t)$ $\newline$ Priya is traveling by train for her job. The equation gives her distance from her destination, $x$ , after $t$ hours. How long will it take for Priya to reach her destination? $\newline$ Choose $1$ answer: $\newline$ (A) $7$ . $7$ hours $\newline$ (B) $\mathbf{1 0 . 1}$ hours $\newline$ (C) $78$ . $0$ hours $\newline$ (D) $600$ . $6$ hours

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Multi-step problems with unit conversions

Full solution

Q.

x=78(7.7-t)

\newline

Priya is traveling by train for her job. The equation gives her distance from her destination,

x

, after

t

hours. How long will it take for Priya to reach her destination?

\newline

Choose

1

answer:

\newline

(A)

7

.

7

hours

\newline

(B)

\mathbf{1 0 . 1}

hours

\newline

(C)

78

.

0

hours

\newline

(D)

600

.

6

hours

Given Equation: We are given the equation $x = 78(7.7 - t)$ which represents Priya's distance from her destination after $t$ hours. To find out how long it will take for Priya to reach her destination, we need to find the value of $t$ when $x$ equals $0$ , because reaching the destination means no distance left to travel.
Set Equal to Zero: Set the equation equal to zero to find when Priya reaches her destination: $0 = 78(7.7 - t)$ .
Divide by $78$ : Divide both sides of the equation by $78$ to isolate the term in parentheses: $\frac{0}{78} = (7.7 - t)$ .
Simplify Equation: Simplify the left side of the equation, knowing that $0$ divided by any number is $0$ : $0 = 7.7 - t$ .
Subtract $7$ . $7$ : To solve for $t$ , we need to get $t$ on one side of the equation by itself. We can do this by subtracting $7.7$ from both sides of the equation: $-7.7 = -t$ .
Multiply by $-1$ : Now, we multiply both sides of the equation by $-1$ to solve for $t$ : $t = 7.7$ .

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