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Julian is using a biking app that compares his position to a simulated biker traveling Julian's target speed. When Julian is behind the simulated biker, he has a negative position. Julian sets the simulated biker to a speed of 20(km)/(h). After he rides his bike for 15 minutes, Julian's app reports a position of -2(1)/(4)km. What has Julian's average speed been so far? (km)/(h)

Julian is using a biking app that compares his position to a simulated biker traveling Julian's target speed. When Julian is behind the simulated biker, he has a negative position.\newlineJulian sets the simulated biker to a speed of 20kmh 20 \frac{\mathrm{km}}{\mathrm{h}} . After he rides his bike for 1515 minutes, Julian's app reports a position of −214 km -2 \frac{1}{4} \mathrm{~km} .\newlineWhat has Julian's average speed been so far?\newlinekmh \frac{\mathrm{km}}{\mathrm{h}}

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Q. Julian is using a biking app that compares his position to a simulated biker traveling Julian's target speed. When Julian is behind the simulated biker, he has a negative position.\newlineJulian sets the simulated biker to a speed of 20kmh 20 \frac{\mathrm{km}}{\mathrm{h}} . After he rides his bike for 1515 minutes, Julian's app reports a position of −214 km -2 \frac{1}{4} \mathrm{~km} .\newlineWhat has Julian's average speed been so far?\newlinekmh \frac{\mathrm{km}}{\mathrm{h}}
  1. Convert Time to Hours: First, we need to convert Julian's biking time from minutes to hours because speed is given in kilometers per hour (km/h).\newline1515 minutes is equivalent to 1560\frac{15}{60} hours.\newline1560=14\frac{15}{60} = \frac{1}{4} hours.
  2. Calculate Distance Traveled: Next, we calculate the distance Julian has actually traveled. Since Julian's position is −214-2 \frac{1}{4} km, it means he is 2142 \frac{1}{4} km behind the simulated biker.\newlineTo find the distance Julian has traveled, we need to consider the distance the simulated biker would have traveled in 14\frac{1}{4} hours at a speed of 2020 km/h.\newlineDistance == Speed ×\times Time\newlineDistance == 2020 km/h ×\times 14\frac{1}{4} h\newlineDistance == 2142 \frac{1}{4}11 km\newlineThis is the distance the simulated biker has traveled.
  3. Find Julian's Distance: Now, we need to find Julian's actual distance traveled. Since Julian is 2142 \frac{1}{4} km behind the simulated biker, we subtract this from the simulated biker's distance.\newlineJulian's distance = Simulated biker's distance - Julian's negative position\newlineJulian's distance = 55 km - 2142 \frac{1}{4} km\newlineTo subtract, we need to convert 2142 \frac{1}{4} to an improper fraction.\newline214=(2×4+1)/4=942 \frac{1}{4} = (2\times4 + 1)/4 = \frac{9}{4} km\newlineJulian's distance = 55 km - 94\frac{9}{4} km\newlineJulian's distance = (204(\frac{20}{4} km - 94\frac{9}{4} km)\newlineJulian's distance = (20−9)/4(20 - 9)/4 km\newlineJulian's distance = 5500 km\newlineJulian's distance = 5511 km
  4. Calculate Average Speed: Finally, we calculate Julian's average speed using the distance he has traveled and the time taken.\newlineAverage speed =DistanceTime= \frac{\text{Distance}}{\text{Time}}\newlineAverage speed =2.75 km(1/4) h= \frac{2.75 \, \text{km}}{(1/4) \, h}\newlineTo divide by a fraction, we multiply by its reciprocal.\newlineAverage speed =2.75 km×(4/1) h= 2.75 \, \text{km} \times (4/1) \, h\newlineAverage speed =11 km/h= 11 \, \text{km/h}\newlineJulian's average speed has been 11 km/h11 \, \text{km/h} so far.

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