1. A rabbit and a turtle are practicing for their big race. The rabbit covers a 30.0 m practice course in 5.00 seconds; the turtle covers the same distance in 120 seconds. If the actual race is run on a 96.0 m course, by how many seconds will the rabbit beat the turtle?


2. Two cyclist race with nearly uniform speed on a 500. m course. The blue bicycle crosses the finish line 2.00 s ahead of the red bicycle. If the red bicycle maintained an average speed of 10.0 m/s, what was the average speed of the blue bicycle?

1. r1=d/t = 30m/5s = 6 m/s.=Speed of rabbit

r2=30m/120s = 0.25 m/s.=Speed of turtle

T1 = d/r1 = 96/6 = 16 s.=Rabbit's time.

T2 = d/r2 = 96/0.25 = 384 s. = Turtle's
time.

T2 - T1 = 384 - 16 = 368 s.

2. T2 = d/r2 = 500/10 = 50 s. = Time of
red bicycle.

d = r1 * T1 = 500
r1 = 500/T1 = 500/(50-2) = 10.42 m/s. =
Speed of blue bicycle.

Thank you

Glad I could help.

1. Well, well, well, looks like the rabbit and the turtle are getting ready for a showdown! Let's calculate who's going to be the champ.

First, let's find out how long it takes for the rabbit to cover the 96.0 m race course. We can set up a proportion here:

30.0 m / 5.00 s = 96.0 m / x

Cross multiply: 30.0 m * x = 5.00 s * 96.0 m
x = (5.00 s * 96.0 m) / 30.0 m
x = 16.0 s

So, the rabbit takes 16.0 seconds to complete the 96.0 m race course.

Now, let's find out how long it takes for the turtle to cover the same distance. We can again set up a proportion:

30.0 m / 120 s = 96.0 m / y

Cross multiply: 30.0 m * y = 120 s * 96.0 m
y = (120 s * 96.0 m) / 30.0 m
y = 384.0 s

So, the turtle takes 384.0 seconds to complete the 96.0 m race course.

Finally, let's find out by how many seconds the rabbit beats the turtle:

16.0 s - 384.0 s = -368.0 s

Well, this is awkward. It seems like the rabbit took negative 368.0 seconds to beat the turtle. Let's just say the rabbit wins by a hare. *wink*

2. Ah, a race between two cyclists! Let's find out how fast that speedy blue bicycle was.

We know that the red bicycle took 10.0 m/s to complete the 500.0 m race course. So, let's find out how long it took for the red bicycle:

t = d / v
t = 500.0 m / 10.0 m/s
t = 50.0 s

So, the red bicycle finished the race in 50.0 seconds.

Now, the blue bicycle finished the same race course 2.0 seconds ahead of the red bicycle. Therefore, the blue bicycle must have finished in:

50.0 s - 2.0 s = 48.0 s

Now, let's find out the average speed of the blue bicycle:

v = d / t
v = 500.0 m / 48.0 s
v ≈ 10.42 m/s

Well, well, well, the blue bicycle had an average speed of approximately 10.42 m/s. Speedy indeed!

1. To find out how many seconds the rabbit will beat the turtle in the actual race, we need to calculate their respective speeds.

First, let's calculate the rabbit's speed. The formula for speed is speed = distance / time. In this case, the rabbit covers a distance of 30.0 m in 5.00 seconds. So, the rabbit's speed is 30.0 m / 5.00 s = 6.00 m/s.

Now, let's calculate the turtle's speed. The turtle covers the same distance of 30.0 meters in 120 seconds. So, the turtle's speed is 30.0 m / 120 s = 0.25 m/s.

Since we know the rabbit's and turtle's speeds, we can find out how long it will take for them to complete the 96.0 m race course.

The time it takes for the rabbit to complete the 96.0 m course can be calculated by dividing the distance by the rabbit's speed: time = distance / speed = 96.0 m / 6.00 m/s = 16.00 s.

Similarly, the time it takes for the turtle to complete the 96.0 m course can be calculated by dividing the distance by the turtle's speed: time = distance / speed = 96.0 m / 0.25 m/s = 384.00 s.

To find out how many seconds the rabbit will beat the turtle, we can subtract the turtle's time from the rabbit's time: beat time = rabbit's time - turtle's time = 16.00 s - 384.00 s = -368.00 s.

However, notice that we obtained a negative value for beat time. This means that in the actual race, the turtle would be ahead of the rabbit. Therefore, the rabbit won't beat the turtle; the turtle will win the race.

2. To find the average speed of the blue bicycle, we need to know the time it takes for it to complete the 500.0 m course and the average speed of the red bicycle.

We are given that the red bicycle maintains an average speed of 10.0 m/s. We also know that the blue bicycle finishes the race 2.00 seconds ahead of the red bicycle.

Let's calculate the time it takes for the red bicycle to finish the race. The formula for time is distance / speed. In this case, the red bicycle covers a distance of 500.0 m and maintains an average speed of 10.0 m/s. So, the time for the red bicycle is 500.0 m / 10.0 m/s = 50.0 s.

Now, let's calculate the time for the blue bicycle. Since it finishes the race 2.00 seconds ahead of the red bicycle, we can subtract 2.00 seconds from the time of the red bicycle: time = 50.0 s - 2.00 s = 48.0 s.

Finally, we can calculate the average speed of the blue bicycle by dividing the distance by the time: speed = distance / time = 500.0 m / 48.0 s ≈ 10.42 m/s.

Therefore, the average speed of the blue bicycle is approximately 10.42 m/s.