- On a sunny day, a tree casts a shadow that is 33 feet long. At the same time, a nearby 4-foot-tall mailbox casts a shadow that is 5.5 feet long. What is the height of the tree? Round your answer to the nearest foot.
A. 24 feet B. 33 feet C. 38 feet D. 45 feet
- Meg can swim 4 laps in 11 minutes. How long should she plan to practice if she needs to swim 10 laps, assuming her speed is constant?
A. 4.4 B. 15.7 C. 22 D. 27.5
Answers and Explanations
- The correct answer is A.
Set up a proportion for the mailbox with the height as the numerator of the fraction and the shadow length as the denominator:
Substitute the given shadow length of the tree into the proportion and let x equal the unknown height of the tree:
Multiply both sides by 33 to solve for x:
Alternatively, you can solve the proportion by cross-multiplying and then dividing both sides by 5:
Choice (A) is the correct answer.
- The correct answer is D.
Set up a proportion with minutes as the numerator of the fraction and the number of laps as the denominator:
Substitute the given number of laps into the proportion, letting x equal the unknown number of minutes:
Multiply both sides by 10 to solve for x, giving you x = 27.5.
Alternatively, you can solve the proportion by cross-multiplying and then dividing both sides of the equation by 4:
Hence, Choice (D) is the correct answer.