Tom and Jerry two brothers decided to go for cycling 2 and 4 to a park which is at distance of 15 km from their house tongue got up early started at 6:00 a.m. only cycle at a speed of 10 km per hour towards the park Jo started cycling towards the park 7:00 a.m. at 20 km per hour both of them reach the park and then come back immediately with the same field at what tom and joe would meet for the first time I am a cat as parent use relative speed concept and explain me do it and similar terms and don't make it much complicated or do not make it much

Let's solve the problem step-by-step to find out when Tom and Joe meet for the first time.

### Key Information

- **Tom's Speed:** 10 km/h
- **Joe's Speed:** 20 km/h
- **Distance to Park:** 15 km
- **Tom starts at:** 6:00 a.m.
- **Joe starts at:** 7:00 a.m.

### Step-by-Step Solution

#### 1. **Calculate Tom's Journey to the Park:**

- **Time Taken by Tom to Reach the Park:**
  \[
  \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{15 \text{ km}}{10 \text{ km/h}} = 1.5 \text{ hours}
  \]

- **Tom Reaches the Park at:**
  - 6:00 a.m. + 1.5 hours = 7:30 a.m.

#### 2. **Calculate Joe's Journey to the Park:**

- **Time Taken by Joe to Reach the Park:**
  \[
  \text{Time} = \frac{15 \text{ km}}{20 \text{ km/h}} = 0.75 \text{ hours} = 45 \text{ minutes}
  \]

- **Joe Reaches the Park at:**
  - 7:00 a.m. + 45 minutes = 7:45 a.m.

### When Tom and Joe Start Returning

- Tom starts returning from the park at 7:30 a.m.
- Joe starts returning from the park at 7:45 a.m.

#### 3. **Find the Time They Meet on the Return Journey:**

**Relative Speed:**
- Since both are moving towards each other on the return trip, we add their speeds to find the relative speed:
  \[
  \text{Relative Speed} = 10 \text{ km/h} + 20 \text{ km/h} = 30 \text{ km/h}
  \]

**Initial Distance Between Them:**
- At 7:45 a.m., when Joe starts returning, Tom is already 15 minutes (or 0.25 hours) into his return trip. So, Tom has already covered:
  \[
  \text{Distance covered by Tom} = 10 \text{ km/h} \times 0.25 \text{ hours} = 2.5 \text{ km}
  \]
  
- This means they are 12.5 km apart when Joe starts his return journey.

**Time Taken to Meet:**
- Using the relative speed, we can calculate the time it takes for them to meet:
  \[
  \text{Time to Meet} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{12.5 \text{ km}}{30 \text{ km/h}} = \frac{12.5}{30} \text{ hours} = 0.4167 \text{ hours} \approx 25 \text{ minutes}
  \]

**Time When They Meet:**
- Joe starts at 7:45 a.m., and they meet 25 minutes later:
  \[
  7:45 \text{ a.m.} + 25 \text{ minutes} = 8:10 \text{ a.m.}
  \]

### Conclusion

Tom and Joe will meet for the first time at **8:10 a.m.** on their way back from the park.

---

Would you like to go through any details or have any questions? Here are some related questions:

1. How do you calculate relative speed when two objects move towards each other?
2. What is the difference between relative speed and actual speed?
3. How can you use the concept of relative speed to solve similar problems?
4. Why does adding the speeds of two objects work when they move towards each other?
5. How do time and distance relate when calculating speed?
6. What would happen if both started their journey at the same time but with different speeds?
7. How does meeting time change if the speeds of the cyclists change?
8. Can you explain how speed affects travel time in a round trip?

**Tip:** When two objects move towards each other, their relative speed is the sum of their individual speeds.

Learn how to solve the problem of Tom and Joe cycling to a park and meeting for the first time using the concept of relative speed. Detailed step-by-step solution provided with calculations for distance, speed, and time. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation