Question 1210215: Hi
Tim and Michelle drove from A to B which was 285km away. Tim set off for B at an average speed of 75km per hour. 48min later Michelle set off for B at a speed of 95km per hour.
How long would Michelle take to catch up with Tim .
How far away was Tim from B when Michelle completed her journey
Found 3 solutions by CPhill, greenestamps, MathTherapy:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down this problem step-by-step:
**Part 1: How long would Michelle take to catch up with Tim?**
1. **Calculate the time Tim traveled before Michelle started:**
- Michelle started 48 minutes later than Tim.
- Convert 48 minutes to hours: 48 minutes / 60 minutes/hour = 0.8 hours.
2. **Calculate the distance Tim traveled before Michelle started:**
- Tim's speed = 75 km/hour
- Time Tim traveled = 0.8 hours
- Distance Tim traveled = speed × time = 75 km/hour × 0.8 hours = 60 km.
3. **Determine the relative speed between Michelle and Tim:**
- Michelle's speed = 95 km/hour
- Tim's speed = 75 km/hour
- Relative speed = Michelle's speed - Tim's speed = 95 km/hour - 75 km/hour = 20 km/hour.
- This is the rate at which Michelle is closing the distance between herself and Tim.
4. **Calculate the time Michelle takes to catch up:**
- Distance Tim was ahead when Michelle started = 60 km
- Relative speed = 20 km/hour
- Time to catch up = Distance / Relative speed = 60 km / 20 km/hour = 3 hours.
**So, Michelle would take 3 hours to catch up with Tim.**
**Part 2: How far away was Tim from B when Michelle completed her journey?**
1. **Calculate the total time Michelle took to reach B:**
- Distance from A to B = 285 km
- Michelle's speed = 95 km/hour
- Time Michelle took = Distance / Speed = 285 km / 95 km/hour = 3 hours.
2. **Calculate the total time Tim traveled when Michelle completed her journey:**
- Tim started 0.8 hours before Michelle.
- Michelle's journey took 3 hours.
- Total time Tim traveled = 0.8 hours + 3 hours = 3.8 hours.
3. **Calculate the distance Tim traveled in 3.8 hours:**
- Tim's speed = 75 km/hour
- Total time Tim traveled = 3.8 hours
- Distance Tim traveled = speed × time = 75 km/hour × 3.8 hours = 285 km.
4. **Calculate the distance Tim was from B when Michelle completed her journey:**
- Distance from A to B = 285 km
- Distance Tim traveled = 285 km
- Distance Tim was from B = Total distance - Distance Tim traveled = 285 km - 285 km = 0 km.
**So, Tim was 0 km away from B (he had just arrived) when Michelle completed her journey.**
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
When Michelle starts her journey, Tim has driven for 48 minutes or 4/5 of an hour at 75 km/h; the distance he has traveled is (4/5)(75) = 60 kilometers. Michelle must make up that distance of 60 km to catch up with Tim.
When both are driving, Tim at 75 km/h and Michelle at 95 km/h, Michelle is catching up with Tim at a rate of (95-75) = 20 km/h. The number of hours it takes her to catch up is then 60/20 = 3.
ANSWER to the first question: It takes Michelle 3 hours to catch up with Tim.
When Michelle catches up with Tim, she has been driving for 3 hours at 95 km/h, covering a distance of 3*95 = 285 km. That is the total distance from A to B, so Michelle catches up to Tim at the time both of them reach B.
ANSWER to the second question: Tim is 0 km from B when Michelle completes her journey.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Hi
Tim and Michelle drove from A to B which was 285km away. Tim set off for B at an average speed of 75km per hour.
48min later Michelle set off for B at a speed of 95km per hour. How long would Michelle take to catch up with Tim.
How far away was Tim from B when Michelle completed her journey
Let time Michelle takes to catch up to Tim, be T
Michelle's and Tim's speeds are 95 k/h and 75 k/h, respectively
So, distance covered by Michelle when she gets to the catch-up point is 95T
Tim left A 48 minutes, or  hr, or  hr before Michelle
Therefore, distance covered by Tim when he gets to the catch-up point is  = 75T + 60
Since they covered the same distance when they met, we equate their distances to get: 95T = 75T + 60
95T - 75T = 60
20T = 60
Time Michelle took to catch up to Tim, or 
In 3 hours, Michelle caught up with Tim. In addition, Michelle completed the 285-km trip in  = 3 hours. So,
Michelle caught up with Tim at the end-point (B). So, both reached B, the end point, at the same time, with Michelle
taking 3 hours, and Tim:  hours, thereby making Tim 0 km from B when Michelle completed the 285-km trek, from A to B.
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