Juan and Rajani are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Juan is 260 miles away from the stadium and Rajani is 380 miles away from the stadium. Juan is driving along the highway at a speed of 30 miles per hour and Rajani is driving at speed of 50 miles per hour. Let JJ represent Juan's distance, in miles, away from the stadium tt hours after noon. Let RR represent Rajani's distance, in miles, away from the stadium tt hours after noon. Graph each function and determine the interval of hours, t, commat, for which Juan is closer to the stadium than Rajani.Click twice to plot each line. Click a line to delete it.1234567891011121314151617181920204060801001201401601802002202402602803003203403603804000Number of Hours After NoonNumber of Miles Away from the Stadiumty0Number of Hours After NoonNumber of Miles Away from the StadiumAnswerAttempt 1 out of 2Juan is closer to the stadium than Rajani when tt .Note: The interval will only apply for valid values of tt in the domain.
Question
Juan and Rajani are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Juan is 260 miles away from the stadium and Rajani is 380 miles away from the stadium. Juan is driving along the highway at a speed of 30 miles per hour and Rajani is driving at speed of 50 miles per hour. Let JJ represent Juan's distance, in miles, away from the stadium tt hours after noon. Let RR represent Rajani's distance, in miles, away from the stadium tt hours after noon. Graph each function and determine the interval of hours, t, commat, for which Juan is closer to the stadium than Rajani.Click twice to plot each line. Click a line to delete it.1234567891011121314151617181920204060801001201401601802002202402602803003203403603804000Number of Hours After NoonNumber of Miles Away from the Stadiumty0Number of Hours After NoonNumber of Miles Away from the StadiumAnswerAttempt 1 out of 2Juan is closer to the stadium than Rajani when tt .Note: The interval will only apply for valid values of tt in the domain.
Solution
The problem involves two people, Juan and Rajani, driving at different speeds and from different distances to the same destination. We are asked to find the interval of time during which Juan is closer to the stadium than Rajani.
First, we need to establish the equations that represent the distance each person is from the stadium at any given time.
For Juan, we know he starts 260 miles away and is driving at 30 miles per hour. Therefore, his distance from the stadium at any given time is given by the equation:
JJ = 260 - 30t
For Rajani, she starts 380 miles away and is driving at 50 miles per hour. Therefore, her distance from the stadium at any given time is given by the equation:
RR = 380 - 50t
We want to find when Juan is closer to the stadium than Rajani, so we want to find when JJ < RR.
Setting the two equations equal to each other gives:
260 - 30t = 380 - 50t
Solving for t gives:
t = (380 - 260) / (50 - 30) = 120 / 20 = 6 hours
Therefore, Juan is closer to the stadium than Rajani 6 hours after noon.
However, we need to check when each of them reaches the stadium to find the valid interval for t.
Juan reaches the stadium when JJ = 0, so 260 - 30t = 0 gives t = 260 / 30 = 8.67 hours
Rajani reaches the stadium when RR = 0, so 380 - 50t = 0 gives t = 380 / 50 = 7.6 hours
Therefore, the valid interval for t when Juan is closer to the stadium than Rajani is 6 hours < t < 7.6 hours.
Similar Questions
LaMarcus is 1400 miles away from home when he starts driving at a rate of 65 miles per hour. As he drives, his distance from home can be modeled by y=65x+1400𝑦=65𝑥+1400 , where x is the time in hours since he left. Bianca is also traveling away from her home, and the function representing her distance from home is parallel to the function representing LaMarcus’s distance. After 5 hours, Bianca is 1525 miles from home. Which function represents Bianca’s distance from home over time?
Rajan and Madan start from a common point and walk straight in the opposite directions. What will be the distance between them at the expiry of three hours?I.Rajan and Madan walk at the speed of 4 km/hr and 6 km/hr respectively.II. Madan walks one and a half times faster than Rajan.
For a training program, Juan rides his bike at anaverage rate of 5.7 minutes per mile. Whichfunction m models the number of minutes it will takeJuan to ride x miles at this rate?A) m x x= 5.7( )B) m x x= + 5.7( )C) m x x= - 5.7( )D) m x x= 5.7
Umapati and Virendranath take 21 minutes and 28 minutes respectively to cover a certain distance L. If they start from two points on a highway which are at a distance of 3L and move towards each other, how many minutes do they take to meet?
Select the correct answerRanjeet drives his car at an average speed of 50 km/hr and reaches his destination in 8 hours. Rehman covers the same distance in 5 hours. If Ranjeet increases his speed by 10 km/hr and Rehman increases his speed by 20 km/hr, then what will be the difference between the times taken by them to reach the destination?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.