Question

6 steve starts on a bicycle ride at 6:00 a.m. and travels at an average rate of 6 miles per hour. two hours later chrissy starts riding the same route at an average speed of 10 miles per hour. which equation could be used to determine when chrissy catches up to steve? a 6h = 10(h - 2) b 6h - 2 = 10h c 6h = 10h + 2 d 6h = 10h - 2 7 jack and jill purchased cell phones. jack signed up for a plan that charges a fee of $24.00 each month plus $0.08 every minute he talks. jills plan charges a fee of $10.00 each month plus $0.15 every minute she talks. which inequality could be used to determine when jills cell phone plan costs more than jacks cell phone plan? a 24m + 0.08m > 10m + 0.15m b 24 + 0.08m < 10 + 0.15m c 24 + 0.08m > 10 + 0.15m d 24m + 0.08m < 10m + 0.15m 8 three times a number is less than or equal to twice the number increased by 20. which inequality could be used to find the number? a 3x ≤ 2x + 20 b 3x < 2x + 20 c 3x < 2x - 20 d 3x ≤ 2x - 20

Explanation:

Step1: Analyze Steve - Chrissy problem

Let $h$ be the number of hours Steve has been riding when Chrissy catches up. Steve's speed is 6 miles per hour, so his distance is $6h$. Chrissy starts 2 hours later, so she rides for $h - 2$ hours at a speed of 10 miles per hour, and her distance is $10(h - 2)$. When Chrissy catches up with Steve, their distances are equal, so the equation is $6h=10(h - 2)$.

Step2: Analyze Jack - Jill problem

Let $m$ be the number of minutes talked. Jack's monthly cost is $24+0.08m$ (a fixed - cost of 24 plus 0.08 per minute). Jill's monthly cost is $10 + 0.15m$ (a fixed - cost of 10 plus 0.15 per minute). We want to find when Jill's cost is more than Jack's, so the inequality is $24+0.08m<10 + 0.15m$.

Step3: Analyze number problem

Let the number be $x$. Three times the number is $3x$, and twice the number increased by 20 is $2x + 20$. The statement "Three times a number is less than or equal to twice the number increased by 20" gives the inequality $3x\leq2x + 20$.

Answer:

1. A. $6h = 10(h - 2)$
2. B. $24 + 0.08m<10 + 0.15m$
3. A. $3x\leq2x + 20$