Cricket Run Rate Calculation for Target Score

This problem involves calculating the required run rate in the remaining overs of a cricket game to achieve a specific target score. We are given the run rate for the initial overs and the total target runs.

Understanding the Initial Situation

• The game has progressed through the first 10 overs.
• The run rate during these first 10 overs was 4.8 runs per over.
• The total target score to be achieved is 348 runs.
• There are 40 overs remaining in the game.

Calculation Steps

To find the required run rate for the remaining 40 overs, we need to follow these steps:

Step 1: Calculate Runs Scored in the First 10 Overs

The runs scored are the product of the number of overs played and the run rate during those overs. Using the formula: $$ \text{Runs Scored} = \text{Overs} \times \text{Run Rate} $$ Plugging in the values: $$ \text{Runs Scored} = 10 \text{ overs} \times 4.8 \text{ runs/over} $$ $$ \text{Runs Scored} = 48 \text{ runs} $$ So, 48 runs were scored in the first 10 overs.

Step 2: Calculate Remaining Runs Needed

Next, we determine how many more runs are needed to reach the target score. Using the formula: $$ \text{Runs Needed} = \text{Target Score} - \text{Runs Scored} $$ Plugging in the values: $$ \text{Runs Needed} = 348 \text{ runs} - 48 \text{ runs} $$ $$ \text{Runs Needed} = 300 \text{ runs} $$ Therefore, 300 runs need to be scored in the remaining overs.

Step 3: Calculate Required Run Rate for Remaining Overs

Finally, we calculate the run rate required over the remaining 40 overs to score the needed 300 runs. Using the formula: $$ \text{Required Run Rate} = \frac{\text{Runs Needed}}{\text{Overs Remaining}} $$ Plugging in the values: $$ \text{Required Run Rate} = \frac{300 \text{ runs}}{40 \text{ overs}} $$ $$ \text{Required Run Rate} = \frac{30}{4} \text{ runs/over} $$ $$ \text{Required Run Rate} = 7.5 \text{ runs/over} $$ The team needs to maintain a run rate of 7.5 in the remaining 40 overs to reach the target score of 348.