The problem in the image involves a person named Ram covering two parts of a journey. The first part is done at a certain speed, and the second part is covered with a different average speed. Let's break it down:

Given Information:

• Ram covers the first part of his journey of 80 km at a certain speed.
• His average speed during the remaining part of the journey is 90 km/h, and it takes him 40 minutes for the second part.
• The overall average speed for the entire journey is 84 km/h.

The goal is to find Ram's speed during the first part of the journey.

Step-by-Step Approach:

1. Total Distance and Average Speed: The total distance covered in the journey is 80 km (from the first part) + the distance covered in the second part. Let's assume the second part distance is $x$ km.

   The total distance is: $80 + x$ km.

   The overall average speed for the entire journey is given as 84 km/h. Using the formula for average speed:

   $\text{Average speed} = \frac{\text{Total Distance}}{\text{Total Time}}$

   So, we have:

   $84 = \frac{80 + x}{\text{Total Time}}$

2. Time for the Second Part: Ram's speed for the second part is 90 km/h, and he takes 40 minutes (which is $\frac{40}{60} = \frac{2}{3}$ hours). The time taken for the second part is:

   $\text{Time for second part} = \frac{x}{90} = \frac{2}{3} \, \text{hours}$

   Solving for $x$, we get:

   $x = 90 \times \frac{2}{3} = 60 \, \text{km}$

3. Total Distance and Time: Now that we know the second part distance is 60 km, the total distance of the journey is:

   $80 + 60 = 140 \, \text{km}$

   Using this, we can calculate the total time using the formula for average speed:

   $84 = \frac{140}{\text{Total Time}}$

   Solving for Total Time:

   $\text{Total Time} = \frac{140}{84} = \frac{5}{3} \, \text{hours}$

4. Time for the First Part: The time taken for the first part is the total time minus the time taken for the second part:

   $\text{Time for first part} = \frac{5}{3} - \frac{2}{3} = 1 \, \text{hour}$

5. Speed for the First Part: Finally, we can calculate the speed for the first part using the formula:

   $\text{Speed for first part} = \frac{\text{Distance}}{\text{Time}} = \frac{80}{1} = 80 \, \text{km/h}$

Answer:

Ram's speed during the first part of his journey was 80 km/h.

If you'd like further details or have any questions about the process, let me know! Here are some related questions to explore further:

1. How do you calculate average speed over multiple segments of a journey?
2. How does time relate to speed when covering different distances?
3. What is the formula for total time when combining two speeds over a journey?
4. How do units (such as minutes to hours) affect speed and time calculations?
5. What happens to average speed if one segment is faster than the other?

Tip: Always convert all time units into hours when dealing with speed in km/h to avoid unit mismatches!