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### 1. Time Taken for a Cricket Ball to Travel 20 Meters
To calculate the time it takes for a bowler to throw a cricket ball at a speed of 110 km/h over a distance of 20 meters, we need to follow these steps:
1. Convert the speed from km/h to m/s:
[tex]\[ \text{Speed (in \( \text{m/s} \))} = \text{Speed (in \( \text{km/h} \))} \times \frac{1000 \, \text{meters}}{3600 \, \text{seconds}} \][/tex]
[tex]\[ = 110 \, \text{km/h} \times \frac{1000}{3600} \approx 30.56 \, \text{m/s} \][/tex]
2. Calculate the time using the formula [tex]\( \text{time} = \frac{\text{distance}}{\text{speed}} \)[/tex]:
[tex]\[ \text{Time} = \frac{20 \, \text{meters}}{30.56 \, \text{m/s}} \approx 0.6545 \, \text{seconds} \][/tex]
So, the ball takes approximately 0.6545 seconds to travel 20 meters.
### 2. Average Speed Needed to Cover a Distance in 2 Hours
To determine the average speed needed to cover the same distance in 2 hours, when a car covers it in 30 minutes with an average speed of 50 km/h, we proceed as follows:
1. Calculate the distance covered in 30 minutes:
[tex]\[ \text{Distance} = 50 \, \text{km/h} \times 0.5 \, \text{hours} = 25 \, \text{km} \][/tex]
2. Calculate the new speed to cover this distance in 2 hours:
[tex]\[ \text{New Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{25 \, \text{km}}{2 \, \text{hours}} = 12.5 \, \text{km/h} \][/tex]
Thus, the average speed needed to cover the distance in 2 hours is 12.5 km/h.
### 3a. Arjun Building the Whole Room Alone
To find out how long it would take for Arjun to build the whole room alone, given the details:
- Rahul alone can build the room in 20 days.
- Rahul works for 5 days, then Arjun finishes the remaining work in 12 days.
1. Calculate the fraction of work done by Rahul in 5 days:
[tex]\[ \text{Rahul's Work in 5 Days} = \frac{5}{20} = 0.25 \][/tex]
2. Remaining Work:
[tex]\[ \text{Remaining Work} = 1 - 0.25 = 0.75 \][/tex]
3. Arjun's rate of work (per day):
[tex]\[ \text{Arjun's Rate} = \frac{0.75}{12} \approx 0.0625 \, \text{(fraction of work per day)} \][/tex]
4. Calculate the time Arjun needs to complete the whole work alone:
[tex]\[ \text{Arjun's Time to Complete Work Alone} = \frac{1}{0.0625} = 16 \, \text{days} \][/tex]
Arjun would take 16 days to build the whole room alone.
### 3b. Rahul and Arjun Working Together from the Beginning
To determine how long it will take if Rahul and Arjun work together from the beginning:
1. Rahul's rate of work (per day):
[tex]\[ \text{Rahul's Rate} = \frac{1}{20} = 0.05 \, \text{(fraction of work per day)} \][/tex]
2. Combined rate of work (Rahul + Arjun):
[tex]\[ \text{Combined Rate} = 0.05 + 0.0625 = 0.1125 \, \text{(fraction of work per day)} \][/tex]
3. Calculate the time using the formula [tex]\( \text{time} = \frac{1}{\text{combined rate}} \)[/tex]:
[tex]\[ \text{Time When Working Together} = \frac{1}{0.1125} \approx 8.89 \, \text{days} \][/tex]
If Rahul and Arjun work together from the beginning, they will take approximately 8.89 days to complete the work.
### 4. Time for Sakshi to Cover the Same Distance at Reduced Speed
To find out how much time Sakshi will take to cover the same distance if she reduces her speed from 8 km/h to 5 km/h:
1. Calculate the distance covered at 8 km/h:
[tex]\[ \text{Distance} = 8 \, \text{km/h} \times 1 \, \text{hour} = 8 \, \text{km} \][/tex]
2. Calculate the new time at a speed of 5 km/h:
[tex]\[ \text{New Time} = \frac{\text{Distance}}{\text{New Speed}} = \frac{8 \, \text{km}}{5 \, \text{km/h}} = 1.6 \, \text{hours} \][/tex]
Converting 1.6 hours to minutes:
[tex]\[ 1.6 \times 60 = 96 \, \text{minutes} \][/tex]
Therefore, Sakshi will take 96 minutes to cover the same distance at a reduced speed of 5 km/h.
To calculate the time it takes for a bowler to throw a cricket ball at a speed of 110 km/h over a distance of 20 meters, we need to follow these steps:
1. Convert the speed from km/h to m/s:
[tex]\[ \text{Speed (in \( \text{m/s} \))} = \text{Speed (in \( \text{km/h} \))} \times \frac{1000 \, \text{meters}}{3600 \, \text{seconds}} \][/tex]
[tex]\[ = 110 \, \text{km/h} \times \frac{1000}{3600} \approx 30.56 \, \text{m/s} \][/tex]
2. Calculate the time using the formula [tex]\( \text{time} = \frac{\text{distance}}{\text{speed}} \)[/tex]:
[tex]\[ \text{Time} = \frac{20 \, \text{meters}}{30.56 \, \text{m/s}} \approx 0.6545 \, \text{seconds} \][/tex]
So, the ball takes approximately 0.6545 seconds to travel 20 meters.
### 2. Average Speed Needed to Cover a Distance in 2 Hours
To determine the average speed needed to cover the same distance in 2 hours, when a car covers it in 30 minutes with an average speed of 50 km/h, we proceed as follows:
1. Calculate the distance covered in 30 minutes:
[tex]\[ \text{Distance} = 50 \, \text{km/h} \times 0.5 \, \text{hours} = 25 \, \text{km} \][/tex]
2. Calculate the new speed to cover this distance in 2 hours:
[tex]\[ \text{New Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{25 \, \text{km}}{2 \, \text{hours}} = 12.5 \, \text{km/h} \][/tex]
Thus, the average speed needed to cover the distance in 2 hours is 12.5 km/h.
### 3a. Arjun Building the Whole Room Alone
To find out how long it would take for Arjun to build the whole room alone, given the details:
- Rahul alone can build the room in 20 days.
- Rahul works for 5 days, then Arjun finishes the remaining work in 12 days.
1. Calculate the fraction of work done by Rahul in 5 days:
[tex]\[ \text{Rahul's Work in 5 Days} = \frac{5}{20} = 0.25 \][/tex]
2. Remaining Work:
[tex]\[ \text{Remaining Work} = 1 - 0.25 = 0.75 \][/tex]
3. Arjun's rate of work (per day):
[tex]\[ \text{Arjun's Rate} = \frac{0.75}{12} \approx 0.0625 \, \text{(fraction of work per day)} \][/tex]
4. Calculate the time Arjun needs to complete the whole work alone:
[tex]\[ \text{Arjun's Time to Complete Work Alone} = \frac{1}{0.0625} = 16 \, \text{days} \][/tex]
Arjun would take 16 days to build the whole room alone.
### 3b. Rahul and Arjun Working Together from the Beginning
To determine how long it will take if Rahul and Arjun work together from the beginning:
1. Rahul's rate of work (per day):
[tex]\[ \text{Rahul's Rate} = \frac{1}{20} = 0.05 \, \text{(fraction of work per day)} \][/tex]
2. Combined rate of work (Rahul + Arjun):
[tex]\[ \text{Combined Rate} = 0.05 + 0.0625 = 0.1125 \, \text{(fraction of work per day)} \][/tex]
3. Calculate the time using the formula [tex]\( \text{time} = \frac{1}{\text{combined rate}} \)[/tex]:
[tex]\[ \text{Time When Working Together} = \frac{1}{0.1125} \approx 8.89 \, \text{days} \][/tex]
If Rahul and Arjun work together from the beginning, they will take approximately 8.89 days to complete the work.
### 4. Time for Sakshi to Cover the Same Distance at Reduced Speed
To find out how much time Sakshi will take to cover the same distance if she reduces her speed from 8 km/h to 5 km/h:
1. Calculate the distance covered at 8 km/h:
[tex]\[ \text{Distance} = 8 \, \text{km/h} \times 1 \, \text{hour} = 8 \, \text{km} \][/tex]
2. Calculate the new time at a speed of 5 km/h:
[tex]\[ \text{New Time} = \frac{\text{Distance}}{\text{New Speed}} = \frac{8 \, \text{km}}{5 \, \text{km/h}} = 1.6 \, \text{hours} \][/tex]
Converting 1.6 hours to minutes:
[tex]\[ 1.6 \times 60 = 96 \, \text{minutes} \][/tex]
Therefore, Sakshi will take 96 minutes to cover the same distance at a reduced speed of 5 km/h.
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