Question

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\,\dfrac{\text{km}}{\text{h}}20 h km ​ 20, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction. After he rides his bike for 151515 minutes, Julian's app reports a position of -2\dfrac{1}{4}\,\text{km}−2 4 1 ​ kmminus, 2, start fraction, 1, divided by, 4, end fraction, start text, k, m, end text. What has Julian's average speed been so far?

Answer 1

11

Explanation:

Answer 2

`\large \boxed{\text{11 km/h}}`

Explanation:

1. The situation after 15 min:

(a) Distance travelled by simulated biker:

15 min =¼ h

`\text{Distance} = (1)/(4)\text{ h} * \frac{\text{20 km}}{\text{1 h}} = \text{5 km}`

(b) Distance travelled by Julian

Julian is 2¼ km behind the biker. The distance he has travelled is (5 - 2¼) km

5 - 2¼ = 5 - ⁹/₄ = ²⁰/₄ - ⁹/₄ = ¹¹/₄ = 2¾

Julian has travelled 2¾ km in ¼ h.

2. Julian's average speed

`\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2(3)/(4)\text{ km}}{(1)/(4)\text{ h}} =(11)/(4)\text{ km}* \frac{4}{\text{1 h}} = \textbf{11 km/h}\\\\\text{Julian's average speed is $\large \boxed{\textbf{11 km/h}}$}`