suppose an auto racer won a 300 mile race with a time of 1:41:48.2942. At one point the racer was 70 miles closer to the finish than the start. how far had the racer gone at that point?
How far from the start was the racer?_miles
x+(x-70) = 300
2x = 370
x = 185
So, he was 185 miles from the start, and 115 miles from the finish.
The whole race took 3600+41*60+48.2942 = 6108.2942 seconds, so
it took 185/300 * 6108.2942 seconds to get that far. Just convert that to hh:mm:ss in the normal way.
To find the distance the racer had gone at the point where they were 70 miles closer to the finish than the start, we need to do the following steps:
1. Convert the time from hours:minutes:seconds to decimal form.
1 hour = 60 minutes, and 1 minute = 60 seconds. So, we can convert the time using the formula:
Time in decimal format = (hours * 60) + minutes + (seconds / 3600)
In this case, the time is 1:41:48.2942. Converting this to decimal, we get:
Time in decimal format = (1 * 60) + 41 + (48.2942 / 3600) = 1.6968 hours
2. Calculate the average speed of the racer throughout the race.
The formula for average speed is:
Average speed = Total distance / Time taken
In this case, we know the time taken is 1.6968 hours, but we don't know the total distance. Let's call the total distance D.
3. Determine the distance from the start when the racer was 70 miles closer to the finish.
At this point, the racer has completed D - 70 miles. We need to find D.
4. Substitute the values into the average speed formula and solve for D.
Average speed = D / 1.6968
Rearranging the formula, we get:
D = Average speed * time taken
We don't have the average speed, but we do have the total distance D in terms of the distance from the start when the racer was 70 miles closer to the finish.
Therefore, we get the equation:
D = (D - 70) / 1.6968
Solving this equation will give us the value of D.
This is the step-by-step process to find the total distance D, which will answer both parts of your question.