a runner leaves at 745 for a morning run at an average speed of 6 mph and returns at 1000 how many miles did he run

HESI A2

HESI A2 Math

1. A runner leaves at 7:45 for a morning run at an average speed of 6 mph and returns at 10:00. How many miles did he run?

A. 11.5 miles
B. 14.5 miles
C. 12 miles
D. 13.5 miles

Correct answer: D

Rationale: The runner left at 7:45 and returned at 10:00, which means he ran for 2 hours and 15 minutes (10:00 - 7:45). At an average speed of 6 mph, in 2.25 hours, he would have covered 6 mph * 2.25 hours = 13.5 miles. Therefore, the correct answer is 13.5 miles. Choices A, B, and C are incorrect because they incorrectly calculate the distance based on the time and speed provided in the question.

2. If Mr. Johnson gives half of his pay to his family, $250 to his landlord, and has exactly 3/7 of his pay left over, how much pay does he receive?

A. $3,600
B. $3,500
C. $2,800
D. $1,750

Correct answer: B

Rationale: Let Mr. Johnson's pay be represented as x. After giving half of his pay to his family, he has x/2 left. Subtracting $250 paid to his landlord, he has x/2 - $250 remaining. Given that this remaining amount is 3/7 of his original pay, the equation becomes x/2 - $250 = 3x/7. Solving this equation shows that x = $3,500. Therefore, Mr. Johnson receives $3,500. Choices A, C, and D are incorrect as they do not align with the correct calculation based on the given conditions in the question.

3. If Gwen's favorite summer drink is 2 parts fruit juice to 3 parts seltzer and she starts with a gallon of fruit juice, how many quarts of seltzer will she need?

A. 3 quarts
B. 4.5 quarts
C. 5 quarts
D. 6 quarts

Correct answer: D

Rationale: To maintain the ratio of 2 parts fruit juice to 3 parts seltzer, for every 2 parts of fruit juice, Gwen will need 3 parts of seltzer. Since a gallon of fruit juice is equivalent to 4 quarts, she will need 3 quarts of seltzer for every 2 quarts of fruit juice. For 4 quarts of fruit juice, she will require 6 quarts of seltzer. Therefore, Gwen will need 6 quarts of seltzer to make the summer drink for her friends. Choice A (3 quarts) is incorrect because it does not account for the correct ratio. Choice B (4.5 quarts) is incorrect because it is not a whole number and does not align with the ratio provided. Choice C (5 quarts) is incorrect as it does not match the proportional ratio of fruit juice to seltzer required.

4. What is the probability of rolling an odd number on a six-sided die?

A. 50%
B. 66.70%
C. 33.30%
D. 25%

Correct answer: A

Rationale: A six-sided die has three odd numbers (1, 3, 5) out of six possible outcomes. To calculate the probability, divide the number of favorable outcomes (odd numbers) by the total number of outcomes: 3/6 = 0.5 or 50%. Therefore, the probability of rolling an odd number on a six-sided die is 50%. Choice A is correct. Choice B (66.70%) is incorrect as it does not represent the correct probability of rolling an odd number on a six-sided die. Choice C (33.30%) is incorrect as it represents the probability of rolling an even number. Choice D (25%) is incorrect as it does not reflect the correct probability of rolling an odd number on a six-sided die.

5. What number is represented by the Roman Numerals XLIV?

A. 34
B. 54
C. 44
D. 24

Correct answer: C

Rationale: In Roman numerals, XL represents 40, and IV represents 4. When XL (40) is combined with IV (4), it forms XLIV, which corresponds to the number 44. Therefore, the correct answer is 44. Choice A (34) is incorrect as it does not consider the value of XL and IV. Choice B (54) is incorrect as it miscalculates the value of XL. Choice D (24) is incorrect as it does not account for the value of XL.