Question

Kate and Lisa are meeting up for coffee this morning, but they had a miscommunication. Kate thinks they're meeting at Lisa's house, and Lisa thinks they're meeting at Kate's house! They both leave their houses at 9:30 A.M. and start the 14.4-mile drive toward each other. At what time will they pass each other if Kate averages 34 miles per hour and Lisa averages 38 miles per hour?

Answer 1

To find the time Kate and Lisa will pass each other, we need to determine how far each one drives until they meet.

1. Calculate the total distance and their speeds:

   • Total distance between them: \( 14.4 \) miles
   • Kate's speed: \( 34 \) miles per hour (mph)
   • Lisa's speed: \( 38 \) mph

2. Calculate the combined speed: The combined speed of both Kate and Lisa is: \[ 34 + 38 = 72 \text{ mph} \]

3. Calculate the time it takes for them to meet: Using the formula for time \( \text{time} = \frac{\text{distance}}{\text{speed}} \), we can find the time it will take them to meet: \[ \text{time} = \frac{14.4 \text{ miles}}{72 \text{ mph}} = 0.2 \text{ hours} \]

4. Convert the time from hours to minutes: Since \( 0.2 \) hours is equivalent to: \[ 0.2 \times 60 = 12 \text{ minutes} \]

5. Determine the meeting time: If Kate and Lisa both leave their houses at \( 9:30 \) A.M., they will pass each other \( 12 \) minutes later: \[ 9:30 \text{ A.M.} + 12 \text{ minutes} = 9:42 \text{ A.M.} \]

Therefore, Kate and Lisa will pass each other at 9:42 A.M.