Question

at 10:00 a.m., pihu and gianna both started running toward each other from opposite ends of a 18 - mile path along a river.
pihu runs at a pace of 13 minutes per mile. gianna runs at a pace of 14 minutes per mile.
show your work here
how many miles does pihu run after 44 minutes? round your answer to the nearest hundredth.
______ miles
how many miles does gianna run after 25 minutes? round your answer to the nearest hundredth.
______ miles
do pihu and gianna meet on the path within 30 minutes?
○ yes ○ no
do pihu and gianna meet on the path within 60 minutes?
○ yes ○ no

Explanation:

Step1: Find Pihu's speed in miles per minute

Pihu's pace is 13 minutes per mile, so her speed \( v_{Pihu} = \frac{1}{13} \) miles per minute.

Step2: Calculate distance Pihu runs in 44 minutes

Using the formula \( d = v \times t \), \( d_{Pihu} = \frac{1}{13} \times 44 \approx 3.38 \) miles.

Step3: Find Gianna's speed in miles per minute

Gianna's pace is 14 minutes per mile, so her speed \( v_{Gianna} = \frac{1}{14} \) miles per minute.

Step4: Calculate distance Gianna runs in 25 minutes

Using \( d = v \times t \), \( d_{Gianna} = \frac{1}{14} \times 25 \approx 1.79 \) miles.

Step5: Check if they meet in 30 minutes

Total distance they need to cover is 18 miles. Combined speed \( v_{total} = \frac{1}{13} + \frac{1}{14} = \frac{14 + 13}{13 \times 14} = \frac{27}{182} \) miles per minute. Time to meet \( t = \frac{18}{\frac{27}{182}} = 18 \times \frac{182}{27} \approx 121.33 \) minutes. So in 30 minutes, they don't meet (No).

Step6: Check if they meet in 60 minutes

Since the meeting time is ~121.33 minutes, which is more than 60, they don't meet in 60 minutes (No).

Answer:

s:

• How many miles does Pihu run after 44 minutes? \( \approx 3.38 \) miles
• How many miles does Gianna run after 25 minutes? \( \approx 1.79 \) miles
• Do Pihu and Gianna meet on the path within 30 minutes? No
• Do Pihu and Gianna meet on the path within 60 minutes? No