QuestionTwo cars start 400 km apart, meet in 2 hours. One is 18 km/h slower. Find the speed of the slower car.

Studdy Solution

STEP 1

Assumptions1. The distance between the two towns is400 kilometers. The two cars start at the same time and travel towards each other3. One car's speed is18 km/h less than the other's4. They meet in hours5. We need to find the speed of the slower car

STEP 2

Let's denote the speed of the faster car as $x$ (in km/h), and the speed of the slower car as $x -18$ (in km/h).

STEP 3

Since the cars are moving towards each other, their relative speed is the sum of their individual speeds. Therefore, in2 hours, they will cover a distance equal to twice the sum of their speeds.
$2(x + (x -18)) =400$

STEP 4

implify the equation.
$2(2x -18) =400$

STEP 5

Expand the left side of the equation.
$4x -36 =400$

STEP 6

Add36 to both sides of the equation to isolate the term with $x$ on one side.
$4x =400 +36$

STEP 7

Calculate the right side of the equation.
$4x =436$

STEP 8

Divide both sides of the equation by4 to solve for $x$ .
$x =436 /4$

STEP 9

Calculate the value of $x$ .
$x =109$

STEP 10

Now that we have the speed of the faster car, we can find the speed of the slower car by subtracting18 from the speed of the faster car.
$x -18 =109 -18$

STEP 11

Calculate the speed of the slower car.
$x -18 =91$ The speed of the slower car is91 km/h.

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QuestionTwo cars start 400 km apart, meet in 2 hours. One is 18 km/h slower. Find the speed of the slower car.

Studdy Solution

STEP 1

Assumptions1. The distance between the two towns is400 kilometers. The two cars start at the same time and travel towards each other3. One car's speed is18 km/h less than the other's4. They meet in hours5. We need to find the speed of the slower car

STEP 2

Let's denote the speed of the faster car as $x$ (in km/h), and the speed of the slower car as $x -18$ (in km/h).

STEP 3

Since the cars are moving towards each other, their relative speed is the sum of their individual speeds. Therefore, in2 hours, they will cover a distance equal to twice the sum of their speeds.
$2(x + (x -18)) =400$

STEP 4

implify the equation.
$2(2x -18) =400$

STEP 5

Expand the left side of the equation.
$4x -36 =400$

STEP 6

Add36 to both sides of the equation to isolate the term with $x$ on one side.
$4x =400 +36$

STEP 7

Calculate the right side of the equation.
$4x =436$

STEP 8

Divide both sides of the equation by4 to solve for $x$ .
$x =436 /4$

STEP 9

Calculate the value of $x$ .
$x =109$

STEP 10

Now that we have the speed of the faster car, we can find the speed of the slower car by subtracting18 from the speed of the faster car.
$x -18 =109 -18$

STEP 11

Calculate the speed of the slower car.
$x -18 =91$ The speed of the slower car is91 km/h.

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QuestionTwo cars start 400 km apart, meet in 2 hours. One is 18 km/h slower. Find the speed of the slower car.

Studdy Solution

STEP 1

Assumptions1. The distance between the two towns is400 kilometers. The two cars start at the same time and travel towards each other3. One car's speed is18 km/h less than the other's4. They meet in hours5. We need to find the speed of the slower car

STEP 2

Let's denote the speed of the faster car as xxx (in km/h), and the speed of the slower car as x−18x -18x−18 (in km/h).

STEP 3

Since the cars are moving towards each other, their relative speed is the sum of their individual speeds. Therefore, in2 hours, they will cover a distance equal to twice the sum of their speeds.2(x+(x−18))=4002(x + (x -18)) =4002(x+(x−18))=400

STEP 4

implify the equation.2(2x−18)=4002(2x -18) =4002(2x−18)=400

STEP 5

Expand the left side of the equation.4x−36=4004x -36 =4004x−36=400

STEP 6

Add36 to both sides of the equation to isolate the term with xxx on one side.4x=400+364x =400 +364x=400+36

STEP 7

Calculate the right side of the equation.4x=4364x =4364x=436

STEP 8

Divide both sides of the equation by4 to solve for xxx.x=436/4x =436 /4x=436/4

STEP 9

Calculate the value of xxx.x=109x =109x=109

STEP 10

Now that we have the speed of the faster car, we can find the speed of the slower car by subtracting18 from the speed of the faster car.x−18=109−18x -18 =109 -18x−18=109−18

STEP 11

Calculate the speed of the slower car.x−18=91x -18 =91x−18=91The speed of the slower car is91 km/h.

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Let's denote the speed of the faster car as $x$ (in km/h), and the speed of the slower car as $x -18$ (in km/h).

Since the cars are moving towards each other, their relative speed is the sum of their individual speeds. Therefore, in2 hours, they will cover a distance equal to twice the sum of their speeds.
$2(x + (x -18)) =400$

implify the equation.
$2(2x -18) =400$

Expand the left side of the equation.
$4x -36 =400$

Add36 to both sides of the equation to isolate the term with $x$ on one side.
$4x =400 +36$

Calculate the right side of the equation.
$4x =436$

Divide both sides of the equation by4 to solve for $x$ .
$x =436 /4$

Calculate the value of $x$ .
$x =109$

Now that we have the speed of the faster car, we can find the speed of the slower car by subtracting18 from the speed of the faster car.
$x -18 =109 -18$

Calculate the speed of the slower car.
$x -18 =91$ The speed of the slower car is91 km/h.