In a race over 4 km Ryan ran at a constant speed. Sophie, however, ran the first 2 km at a speed 1 km/h more than Ryan and ran the second 2 km at a speed 1 km/h less than Ryan.
Who won the race?
If Ryan's speed was r, then since time = distance/speed, compare
4/r and 2/(r-1)+2/(r+1)
This is easy, since it just involves comparing
4r/r^2 and 4r/(r^2-1)
Well, it seems like Ryan and Sophie were in quite the speed competition! But let's break it down. Ryan ran at a constant speed for the entire race, while Sophie decided to change things up. She ran the first 2 km faster than Ryan, but then slowed down for the last 2 km. Now, I don't want to be the one to burst Sophie's bubble, but consistency is key in a race. So, my vote goes to Ryan! He may not have had the fastest individual speed, but he stayed steady throughout the entire race. Keep it up, Ryan!
To determine who won the race, we need to compare the total time taken by both Ryan and Sophie to complete the 4 km race.
Let's assume Ryan's speed is x km/h. According to the given information:
Ryan's speed for the entire race = x km/h
Sophie's speed for the first 2 km = (x + 1) km/h
Sophie's speed for the second 2 km = (x - 1) km/h
To calculate the time taken by each runner, we can use the formula: Time = Distance / Speed.
Ryan's time for the entire race = 4 km / x km/h
Sophie's time for the first 2 km = 2 km / (x + 1) km/h
Sophie's time for the second 2 km = 2 km / (x - 1) km/h
Now, let's compare their times:
Ryan's total time = 4 km / x km/h
Sophie's total time = (2 km / (x + 1) km/h) + (2 km / (x - 1) km/h)
To determine who won the race, we need to compare their total times. If Ryan's total time is shorter, he won the race. If Sophie's total time is shorter, she won the race.
By comparing their total times, we can determine the winner.
To determine who won the race, we need to compare the times it took for Ryan and Sophie to complete the 4 km distance.
Let's start by finding the time it took Ryan to run the entire 4 km distance.
Since Ryan ran at a constant speed, we can assume his speed for the entire race is 'x' km/h.
Using the formula: Time = Distance / Speed, we can calculate Ryan's time for the 4 km race.
Time taken by Ryan = 4 km / x km/h
Now let's calculate Sophie's time for the race.
For the first 2 km, Sophie ran at a speed 1 km/h more than Ryan's speed. So her speed can be represented as 'x + 1' km/h.
Using the same formula as before, we find Sophie's time for the first 2 km:
Time taken by Sophie for first 2 km = 2 km / (x + 1) km/h
For the second 2 km, Sophie ran at a speed 1 km/h less than Ryan's speed. So her speed can be represented as 'x - 1' km/h.
Similarly, we find Sophie's time for the second 2 km:
Time taken by Sophie for the second 2 km = 2 km / (x - 1) km/h
Now, let's calculate Sophie's total time for the entire race by summing her times for the first and second 2 km:
Total time taken by Sophie = Time taken by Sophie for first 2 km + Time taken by Sophie for second 2 km
Comparing Ryan's time and Sophie's total time will help us determine the winner.
If Ryan's time is lesser than Sophie's total time, Ryan wins the race. If Sophie's total time is lesser, she wins the race.
By comparing their times, we can determine the winner of the race.