$6$ . Wei drives at an average speed of $x \mathrm{~km} / \mathrm{h}$ for $2$ hours $40$ minutes and then at an average of speed of $y \mathrm{~km} / \mathrm{h}$ for $1$ hour $20$ minutes. He drives a total distance of $240 \mathrm{~km}$ . $\newline$ [ $2015$ P $2$ Q $6$ ] $\newline$ (a) Write down an equation in $x$ and $y$ to represent this information and show that it simplifies to $\newline$ $2 x+y=180$

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Grade 6

Solve one-step multiplication and division equations: word problems

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6

. Wei drives at an average speed of

x \mathrm{~km} / \mathrm{h}

for

2

hours

40

minutes and then at an average of speed of

y \mathrm{~km} / \mathrm{h}

for

1

hour

20

minutes. He drives a total distance of

240 \mathrm{~km}

\newline

[

2015

2

6

]

\newline

(a) Write down an equation in

x

and

y

to represent this information and show that it simplifies to

\newline

2 x+y=180

Write Equation for Total Distance: question_prompt: Write down an equation in $x$ and $y$ to represent Wei's total driving distance and show that it simplifies to $2x + y = 180$ .
Calculate Driving Distance at $x$ km/h: Wei drives for $2$ hours $40$ minutes at $x$ km/h. Convert $2$ hours $40$ minutes to hours by dividing $40$ by $60$ . $\frac{40}{60} = \frac{2}{3}$ hours. So, $2$ hours $40$ minutes is $2$ $1$ hours.
Calculate Driving Distance at $y$ km/h: Calculate the distance Wei drives at $x$ km/h. Distance = speed $\times$ time, so the distance is $x$ km/h $\times \frac{8}{3}$ hours.
Calculate Total Distance: Wei then drives for $1$ hour $20$ minutes at $y$ km/h. Convert $1$ hour $20$ minutes to hours by dividing $20$ by $60$ . $\frac{20}{60} = \frac{1}{3}$ hours. So, $1$ hour $20$ minutes is $20$ $0$ hours.
Set Total Distance Equation: Calculate the distance Wei drives at $y$ km/h. Distance = speed $\times$ time, so the distance is $y$ km/h $\times$ $\frac{4}{3}$ hours.
Simplify Equation: Add the two distances together to get the total distance. The total distance is $x \, \text{km/h} \times \frac{8}{3} \, \text{hours} + y \, \text{km/h} \times \frac{4}{3} \, \text{hours}.$
Multiply to Eliminate Fractions: Wei drives a total distance of $240\,\text{km}$ . Set the equation $x\,\text{km/h} \times \frac{8}{3}\,\text{hours} + y\,\text{km/h} \times \frac{4}{3}\,\text{hours} = 240\,\text{km}$ .
Final Simplified Equation: Simplify the equation. Multiply both sides of the equation by $3$ to get rid of the fractions. $3(x \, \text{km/h} \times \frac{8}{3} \, \text{hours}) + 3(y \, \text{km/h} \times \frac{4}{3} \, \text{hours}) = 3 \times 240 \, \text{km}.$
Final Simplified Equation: Simplify the equation. Multiply both sides of the equation by $3$ to get rid of the fractions. $3(x \, \text{km/h} \times \frac{8}{3} \, \text{hours}) + 3(y \, \text{km/h} \times \frac{4}{3} \, \text{hours}) = 3 \times 240 \, \text{km}$ . After multiplying, the equation becomes $8x \, \text{km} + 4y \, \text{km} = 720 \, \text{km}$ .
Final Simplified Equation: Simplify the equation. Multiply both sides of the equation by $3$ to get rid of the fractions. $3(x \, \text{km/h} \times \frac{8}{3} \, \text{hours}) + 3(y \, \text{km/h} \times \frac{4}{3} \, \text{hours}) = 3 \times 240 \, \text{km}$ . After multiplying, the equation becomes $8x \, \text{km} + 4y \, \text{km} = 720 \, \text{km}$ . Divide the entire equation by $4$ to simplify it further. $\frac{8x \, \text{km}}{4} + \frac{4y \, \text{km}}{4} = \frac{720 \, \text{km}}{4}$ .
Final Simplified Equation: Simplify the equation. Multiply both sides of the equation by $3$ to get rid of the fractions. $3(x \, \text{km/h} \times \frac{8}{3} \, \text{hours}) + 3(y \, \text{km/h} \times \frac{4}{3} \, \text{hours}) = 3 \times 240 \, \text{km}$ . After multiplying, the equation becomes $8x \, \text{km} + 4y \, \text{km} = 720 \, \text{km}$ . Divide the entire equation by $4$ to simplify it further. $(8x \, \text{km})/4 + (4y \, \text{km})/4 = 720 \, \text{km}/4$ . The simplified equation is $2x \, \text{km} + y \, \text{km} = 180 \, \text{km}$ .