amal can run ⅛ mile in 1 ½ minutes. a. if he can maintain that pace, how long will it take him to run 1…

amal can run ⅛ mile in 1 ½ minutes. a. if he can maintain that pace, how long will it take him to run 1 mile? b. how long would it take amal to run 3 miles at that pace? c. naomi can run ¼ mile in 2 minutes. does amal or naomi run faster? how do you know?

amal can run ⅛ mile in 1 ½ minutes. a. if he can maintain that pace, how long will it take him to run 1 mile? b. how long would it take amal to run 3 miles at that pace? c. naomi can run ¼ mile in 2 minutes. does amal or naomi run faster? how do you know?

Answer

Explanation:

Step1: Calculate Amal's speed per mile

Amal runs $\frac{1}{8}$ mile in $1\frac{1}{2}$ minutes. First convert $1\frac{1}{2}$ to an improper - fraction: $1\frac{1}{2}=\frac{3}{2}$ minutes. The speed formula is $v = \frac{d}{t}$. To find the time per mile for Amal, we use the reciprocal. If $t_1$ is the time for $\frac{1}{8}$ mile, then for 1 mile, $t_{Amal}= \frac{3}{2}\times8 = 12$ minutes per mile.

Step2: Calculate Naomi's speed per mile

Naomi runs $\frac{1}{4}$ mile in 2 minutes. Using the speed - time relationship, if $t_2$ is the time for $\frac{1}{4}$ mile, then for 1 mile, $t_{Naomi}=2\times4 = 8$ minutes per mile.

Step3: Compare their speeds

Since Naomi takes 8 minutes per mile and Amal takes 12 minutes per mile, Naomi runs faster.

Answer:

C. Naomi can run $\frac{1}{4}$ mile in 2 minutes. Does Amal or Naomi run faster?