This is the question.
In 1991, an American, Ann Trason, set a world record by running 100 km in 7hr,50min,09sec.
What is the best estimate of her average speed?
A.12 km per hour
B.14 km per hour
C.16 km per hour
D.18 km per hour
how do u figure this out? im stuck on this. im very thnkful 2 u if u just show me wat i m supposed to do. thx again :)
that is about 8 hours
100 km / 8 hours = about 12 and a half
thnk u.
To find the best estimate of Ann Trason's average speed, we need to calculate the average speed by dividing the distance covered by the time taken.
First, let's convert Ann Trason's time from hours, minutes, and seconds to just hours. To do this, we need to convert the minutes and seconds to fractions of an hour.
Since there are 60 minutes in an hour, we can divide the number of minutes by 60 to get the fraction in hours. In this case, Ann Trason's 50 minutes can be expressed as 50/60 = 5/6 hours.
Similarly, there are 60 seconds in a minute, so we divide the number of seconds by 3600 (60 minutes x 60 seconds). Ann Trason's 9 seconds can be expressed as 9/3600 = 1/400 hours.
Now, we can add up the total time in hours:
7 hours + 5/6 hours + 1/400 hours = 7 5/6 + 1/400 hours.
Next, we convert the time to a decimal form for easier calculation. To do this, we convert the mixed fraction 7 5/6 to an improper fraction.
To convert 7 5/6 to an improper fraction:
Multiply the whole number (7) by the denominator of the fraction (6), and add the numerator (5). So, 7 × 6 + 5 = 42 + 5 = 47.
Now, the improper fraction is 47/6 + 1/400.
To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple (LCM) of 6 and 400 is 2400.
So, let's convert the fractions to have a common denominator of 2400:
47/6 = (47/6) × (400/400) = 18800/2400, and
1/400 = (1/400) × (6/6) = 6/2400.
Now, we can add the fractions:
18800/2400 + 6/2400 = 18806/2400.
Simplifying this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
18806/2400 ÷ 2/2 = 9403/1200.
Now, we have the time in decimal form: 9403/1200 hours.
Finally, we find the average speed by dividing the distance (100 km) by the time (9403/1200 hours):
100 km ÷ (9403/1200 hours) = 100 km × (1200/9403 hours).
To simplify this calculation, we multiply both numerator and denominator by a common factor (10):
1000 km × (120/940.3 hours) = 120,000/940.3 km per hour.
Now, we can round this decimal to the nearest whole number to find the best estimate for Ann Trason's average speed:
120,000/940.3 ≈ 127.82 km per hour.
Rounded to the nearest whole number, Ann Trason's average speed is approximately 128 km per hour.
Looking at the answer choices provided, the closest estimate is 12 km per hour, option A.
Therefore, the best estimate of Ann Trason's average speed is 12 km per hour, option A.