To find the man's speed in meters per second, we need to determine the total time taken and then calculate the speed using the given distance.
Let's break down the information provided:
Total distance = 24 km
Time taken = 1 hour and 40 minutes
To convert 1 hour and 40 minutes to hours: 1 hour = 60 minutes 40 minutes = 40/60 = 2/3 hours
Total time taken = 1 hour + 2/3 hours = 5/3 hours
Let's denote the remaining distance as D.
According to the given information, the distance covered by the man after 1 hour and 40 minutes is 5/7 of the remaining distance:
5/7 * D = 24 km - D
Multiplying both sides by 7 to eliminate the fraction:
5D = 168 km - 7D
Combining like terms:
12D = 168 km
D = 168 km / 12 = 14 km
Therefore, the remaining distance (D) is 14 km.
Now we can calculate the total time taken to cover the entire distance of 24 km:
Total time = Time taken initially + Time taken to cover the remaining distance Total time = 1 hour and 40 minutes + Time taken to cover 14 km
Converting 1 hour and 40 minutes to hours: 40 minutes = 40/60 = 2/3 hours
Total time = 1 hour + 2/3 hours + Time taken to cover 14 km
Now we can calculate the speed in meters per second:
Speed = Distance / Time Speed = 24 km / (Total time in hours * conversion factor to seconds)
Total time in hours = 1 hour + 2/3 hours + Time taken to cover 14 km
Conversion factor from hours to seconds: 1 hour = 3600 seconds
Speed = 24 km / ((1 + 2/3) hours * 3600 seconds/hour)
Calculating the speed:
Speed = 24 km / (5/3 hours * 3600 seconds/hour) Speed = (24 * 3) / (5 * 3600) km/s Speed = 72 / 18000 km/s
Converting km/s to meters/second: 1 km = 1000 meters
Speed = (72 / 18000) km/s * (1000 meters/km) Speed = 0.004 m/s
Therefore, the man's speed is 0.004 meters per second.