QuestionYu Yan's triathlon: swim 0.5 miles in 25 min. Find avg. speed in miles/min and miles/hour. Write distance equations for swim and bike.

Studdy Solution

STEP 1

Assumptions1. The swim distance is0.5 miles. The swim time is25 minutes3. The bike ride distance is12.4 miles4. The bike ride time is48 minutes5. The length of the pier is0. miles6. Speed is calculated as distance divided by time

STEP 2

First, we need to find Yu Yan's average swimming speed in miles per minute. We can do this by dividing the swim distance by the swim time.
$Speed = \frac{Distance}{Time}$

STEP 3

Now, plug in the given values for the swim distance and swim time to calculate the speed.
$Speed = \frac{0.5\, miles}{25\, minutes}$

STEP 4

Calculate the speed.
$Speed = \frac{0.\, miles}{25\, minutes} =0.02\, miles/minute$

STEP 5

Next, we need to find Yu Yan's average swimming speed in miles per hour. We can do this by multiplying the speed in miles per minute by60 (since there are60 minutes in an hour).
$Speed =0.02\, miles/minute \times60\, minutes/hour$

STEP 6

Calculate the speed in miles per hour.
$Speed =0.02\, miles/minute \times60\, minutes/hour =1.2\, miles/hour$

STEP 7

Now, let's write an equation relating the total distance Yu Yan swims $d$ in miles to the number of minutes she swims $m$ . We know that $d = speed \times time$ , so we can write $d =0.02m$

STEP 8

Next, let's write an equation relating the total distance Yu Yan swims $d$ in miles to the number of hours she swims $h$ . We know that $d = speed \times time$ , so we can write $d =1.2h$

STEP 9

Now, let's find out how many minutes it takes Yu Yan to reach the end of the pier. We can do this by dividing the length of the pier by her average speed.
$Time = \frac{Distance}{Speed}$

STEP 10

Plug in the values for the distance and the speed to calculate the time.
$Time = \frac{0.2\, miles}{0.02\, miles/minute}$

STEP 11

Calculate the time it takes for Yu Yan to reach the end of the pier.
$Time = \frac{0.\, miles}{0.02\, miles/minute} =10\, minutes$

STEP 12

Next, we need to find Yu Yan's average biking speed in miles per hour. We can do this by dividing the bike ride distance by the bike ride time and then multiplying by60 to convert minutes to hours.
$Speed = \frac{Distance}{Time} \times60$

STEP 13

Now, plug in the given values for the bike ride distance and bike ride time to calculate the speed.
$Speed = \frac{12.\, miles}{48\, minutes} \times60$

STEP 14

Calculate the speed in miles per hour.
$Speed = \frac{12.4\, miles}{48\, minutes} \times60 =.\, miles/hour$

STEP 15

Finally, let's write an equation relating the total distance Yu Yan bikes $d$ in miles to the number of hours she bikes $h$ . We know that $d = speed \times time$ , so we can write $d =15.5h$ Yu Yan's average swimming speed is0.02 miles per minute or.2 miles per hour. It takes her10 minutes to swim the length of the pier. Her average biking speed is15.5 miles per hour.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms