Calculating Peter's Maximum Time to Cover Distance
To calculate the greatest possible time taken by Peter to cover the distance, we should consider the smallest possible speed and the largest possible distance within the given significant figures, as time is inversely proportional to speed.
The distance of 3800 km is given to two significant figures, which means it could be anywhere from 3750 km (which would round up to 3800 km) to 3849 km (which would round down to 3800 km). So we take the higher value of 3849 km for the greatest possible time.
The speed of 190 km/h is given correct to the nearest ten kilometers per hour. This means the actual speed could be anywhere from 185 km/h (which would round up to 190 km/h) to 194 km/h (which would round down to 190 km/h). So we take the lower value of 185 km/h for the greatest possible time.
Now, to find the time taken, we use the formula:
Time = Distance / Speed
Using the largest distance and smallest speed, we get:
Time = 3849 km / 185 km/h
To find the time in hours, we divide:
Time = 3849 / 185 ≈ 20.8 hours
Now we need to convert the time to seconds. There are 3600 seconds in an hour, so:
Time in seconds = 20.8 hours * 3600 seconds/hour
≈ 74880 seconds
However, we need to give the answer correct to three significant figures. The figure 74880 has five significant figures, so rounding to three significant figures, we would have:
Time ≈ 74900 seconds
Therefore, the greatest possible time taken by Peter to cover the whole distance, correct to three significant figures, is approximately 74900 seconds.
