QuestionChang's trip to the mountains took 7 hours; the return took 5 hours at 18 mph faster. Find the distance to the mountains.

Studdy Solution

STEP 1

Assumptions1. The time taken to drive to the mountains is7 hours. . The time taken to drive back home is5 hours.
3. The average speed while driving back home was18 miles per hour faster than the speed while driving to the mountains.
4. The distance from Chang's home to the mountains is the same both ways.

STEP 2

Let's denote the speed at which Chang drove to the mountains as $s$ (in miles per hour). Then, the speed at which he drove back home is $s +18$ miles per hour.

STEP 3

The distance to the mountains can be calculated by multiplying the speed by the time taken. Therefore, the distance to the mountains when Chang drove there is $s \\times7$ .

STEP 4

Similarly, the distance from the mountains to Chang's home when he drove back is $(s +18) \\times$ .

STEP 5

Since the distance to the mountains and back is the same, we can set these two expressions equal to each other and solve for $s$ .
$s \\times7 = (s +18) \\times5$

STEP 6

Expand the right side of the equation.
$s =5s +90$

STEP 7

Subtract $5s$ from both sides of the equation.
$2s =90$

STEP 8

Divide both sides of the equation by2 to solve for $s$ .
$s =45$

STEP 9

Now that we have the speed at which Chang drove to the mountains, we can find the distance to the mountains by multiplying this speed by the time taken to drive there.
$Distance = s \\times Time$

STEP 10

Plug in the values for $s$ and the time to calculate the distance.
$Distance =45 \\times7$

STEP 11

Calculate the distance.
$Distance =45 \\times7 =315$ Chang lives315 miles away from the mountains.

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QuestionChang's trip to the mountains took 7 hours; the return took 5 hours at 18 mph faster. Find the distance to the mountains.

Studdy Solution

STEP 1

STEP 2

Let's denote the speed at which Chang drove to the mountains as $s$ (in miles per hour). Then, the speed at which he drove back home is $s +18$ miles per hour.

STEP 3

The distance to the mountains can be calculated by multiplying the speed by the time taken. Therefore, the distance to the mountains when Chang drove there is $s \\times7$ .

STEP 4

Similarly, the distance from the mountains to Chang's home when he drove back is $(s +18) \\times$ .

STEP 5

Since the distance to the mountains and back is the same, we can set these two expressions equal to each other and solve for $s$ .
$s \\times7 = (s +18) \\times5$

STEP 6

Expand the right side of the equation.
$s =5s +90$

STEP 7

Subtract $5s$ from both sides of the equation.
$2s =90$

STEP 8

Divide both sides of the equation by2 to solve for $s$ .
$s =45$

STEP 9

Now that we have the speed at which Chang drove to the mountains, we can find the distance to the mountains by multiplying this speed by the time taken to drive there.
$Distance = s \\times Time$

STEP 10

Plug in the values for $s$ and the time to calculate the distance.
$Distance =45 \\times7$

STEP 11

Calculate the distance.
$Distance =45 \\times7 =315$ Chang lives315 miles away from the mountains.

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QuestionChang's trip to the mountains took 7 hours; the return took 5 hours at 18 mph faster. Find the distance to the mountains.

Studdy Solution

STEP 1

STEP 2

Let's denote the speed at which Chang drove to the mountains as sss (in miles per hour). Then, the speed at which he drove back home is s+18s +18s+18 miles per hour.

STEP 3

The distance to the mountains can be calculated by multiplying the speed by the time taken. Therefore, the distance to the mountains when Chang drove there is stimes7s \\times7stimes7.

STEP 4

Similarly, the distance from the mountains to Chang's home when he drove back is (s+18)times(s +18) \\times(s+18)times.

STEP 5

Since the distance to the mountains and back is the same, we can set these two expressions equal to each other and solve for sss.stimes7=(s+18)times5s \\times7 = (s +18) \\times5stimes7=(s+18)times5

STEP 6

Expand the right side of the equation.s=5s+90s =5s +90s=5s+90

STEP 7

Subtract 5s5s5s from both sides of the equation.2s=902s =902s=90

STEP 8

Divide both sides of the equation by2 to solve for sss.s=45s =45s=45

STEP 9

Now that we have the speed at which Chang drove to the mountains, we can find the distance to the mountains by multiplying this speed by the time taken to drive there.Distance=stimesTimeDistance = s \\times TimeDistance=stimesTime

STEP 10

Plug in the values for sss and the time to calculate the distance.Distance=45times7Distance =45 \\times7Distance=45times7

STEP 11

Calculate the distance.Distance=45times7=315Distance =45 \\times7 =315Distance=45times7=315Chang lives315 miles away from the mountains.

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Let's denote the speed at which Chang drove to the mountains as $s$ (in miles per hour). Then, the speed at which he drove back home is $s +18$ miles per hour.

The distance to the mountains can be calculated by multiplying the speed by the time taken. Therefore, the distance to the mountains when Chang drove there is $s \\times7$ .

Similarly, the distance from the mountains to Chang's home when he drove back is $(s +18) \\times$ .

Since the distance to the mountains and back is the same, we can set these two expressions equal to each other and solve for $s$ .
$s \\times7 = (s +18) \\times5$

Expand the right side of the equation.
$s =5s +90$

Subtract $5s$ from both sides of the equation.
$2s =90$

Divide both sides of the equation by2 to solve for $s$ .
$s =45$

Now that we have the speed at which Chang drove to the mountains, we can find the distance to the mountains by multiplying this speed by the time taken to drive there.
$Distance = s \\times Time$

Plug in the values for $s$ and the time to calculate the distance.
$Distance =45 \\times7$

Calculate the distance.
$Distance =45 \\times7 =315$ Chang lives315 miles away from the mountains.