To solve this problem, we can set up a proportion using the given information.
Let x represent the number of stories in the building.
The proportion can be set up as:
(shadow length of 7-story building) / (height of 7-story building) = (shadow length of x-story building) / (height of x-story building)
Substituting the given values:
27.65m / 7 stories = 19.75m / x stories
To solve for x, we cross-multiply:
27.65 * x = 19.75 * 7
27.65x = 138.25
Dividing both sides of the equation by 27.65:
x = 5
Therefore, a building that casts a 19.75m long shadow would be approximately 5 stories high.
when looking at two buildings at the same time length of the buildings' shadows varies directly as their height, meaning there is a rate of shadow length per building height. If a 7-story building has a 27.65 m long shadow, using a proportion determine how many stories high would a building be if it casts a shadow that is 19.75 m long.
Show all calculations, steps, and/ or explain your answer.
5 answers
when looking at two buildings at the same time length of the buildings' shadows varies directly as their height, meaning there is a rate of shadow length per building height. If a 7-story building has a 27.65 m long shadow, using a proportion determine how many stories high would a building be if it casts a shadow that is 19.75 m long with all diagram
Show all calculations, steps, and/ or explain your answer.
Show all calculations, steps, and/ or explain your answer.
To solve this problem using a proportion, we can set up the equation:
(shadow length of building 1) / (height of building 1) = (shadow length of building 2) / (height of building 2)
Let's label the variables:
Shadow length of building 1 = S1
Height of building 1 = H1
Shadow length of building 2 = S2
Height of building 2 = H2
Given:
S1 = 27.65 m (shadow length of the 7-story building)
H1 = 7 stories (height of the 7-story building)
S2 = 19.75 m (shadow length for the building we want to find the height of)
H2 = ?
Using the proportion equation, we have:
S1 / H1 = S2 / H2
Substituting the given values:
27.65 / 7 = 19.75 / H2
To solve for H2, we cross-multiply:
27.65 * H2 = 19.75 * 7
27.65H2 = 138.25
Dividing both sides of the equation by 27.65 to solve for H2:
H2 = 5
Therefore, the building that casts a 19.75m long shadow would be approximately 5 stories high.
(shadow length of building 1) / (height of building 1) = (shadow length of building 2) / (height of building 2)
Let's label the variables:
Shadow length of building 1 = S1
Height of building 1 = H1
Shadow length of building 2 = S2
Height of building 2 = H2
Given:
S1 = 27.65 m (shadow length of the 7-story building)
H1 = 7 stories (height of the 7-story building)
S2 = 19.75 m (shadow length for the building we want to find the height of)
H2 = ?
Using the proportion equation, we have:
S1 / H1 = S2 / H2
Substituting the given values:
27.65 / 7 = 19.75 / H2
To solve for H2, we cross-multiply:
27.65 * H2 = 19.75 * 7
27.65H2 = 138.25
Dividing both sides of the equation by 27.65 to solve for H2:
H2 = 5
Therefore, the building that casts a 19.75m long shadow would be approximately 5 stories high.
Jack went on a hike for 2 hours and 15 minutes. According to his fitness watch, he burned 1013 calories during the hike. Brooke went to a 45 minutes high-impact aerobic class. According to her fitness watch, she burned 347 calories. Compare the rate at which jack and brooke burn calories. Conclude who burns calories at a higher rate.
Show all calculations, steps, and/ or explain your answer.
Show all calculations, steps, and/ or explain your answer.
To compare the rate at which Jack and Brooke burn calories, we can calculate their calorie burn rates per minute.
Jack's hike duration: 2 hours 15 minutes = 2 * 60 minutes + 15 minutes = 135 minutes
Jack's calorie burn rate: 1013 calories / 135 minutes = 7.505 calories/minute
Brooke's aerobic class duration: 45 minutes
Brooke's calorie burn rate: 347 calories / 45 minutes = 7.711 calories/minute
Comparing the calorie burn rates, we see that Brooke burns calories at a higher rate of 7.711 calories per minute compared to Jack's rate of 7.505 calories per minute. Therefore, Brooke burns calories at a higher rate than Jack.
Jack's hike duration: 2 hours 15 minutes = 2 * 60 minutes + 15 minutes = 135 minutes
Jack's calorie burn rate: 1013 calories / 135 minutes = 7.505 calories/minute
Brooke's aerobic class duration: 45 minutes
Brooke's calorie burn rate: 347 calories / 45 minutes = 7.711 calories/minute
Comparing the calorie burn rates, we see that Brooke burns calories at a higher rate of 7.711 calories per minute compared to Jack's rate of 7.505 calories per minute. Therefore, Brooke burns calories at a higher rate than Jack.