Rational number word problems

Google Classroom

Problem

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, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction. After he rides his bike for $15$15 minutes, Julian's app reports a position of $-2\dfrac{1}{4}\,\text{km}$minus, 2, start fraction, 1, divided by, 4, end fraction, start text, k, m, end text.

What has Julian's average speed been so far?

 $\dfrac{\text{km}}{\text{h}}$start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction

Hint #11 / 5

We can use the distance the simulated biker has traveled to figure out how far Julian has traveled. Then we can find his average speed.

Hint #22 / 5

The simulated biker has traveled $20\,\dfrac{\text{km}}{\text{h}}$20, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction for $15$15 minutes. There are $60$60 minutes in $1$1 hour.

$\begin{aligned} \text{distance}&=\text{speed}\times \text{time}\\\\ &=20\,\dfrac{\text{km}}{\text{h}} \times 15\,\text{min}\\\\ &=20\,\dfrac{\text{km}}{\cancel{\text{h}}} \times 15\,\cancel{\text{min}}\times \dfrac{1\,\cancel{\text{h}}}{60\,\cancel{\text{min}}}\\\\ &=\dfrac{300}{60}\,\text{km}\\\\ &=5\,\text{km} \end{aligned}$

The simulated biker has traveled $5\,\text{km}$5, start text, k, m, end text.

Hint #33 / 5

Julian's position is $-2\dfrac{1}{4}$minus, 2, start fraction, 1, divided by, 4, end fraction, which means he has traveled $2\dfrac{1}{4}\,\text{km}$2, start fraction, 1, divided by, 4, end fraction, start text, k, m, end text less than the simulated biker has.

$5-2\dfrac{1}{4}=2\dfrac{3}{4}$5, minus, 2, start fraction, 1, divided by, 4, end fraction, equals, 2, start fraction, 3, divided by, 4, end fraction

Julian has traveled $2\dfrac{3}{4}\,\text{km}$2, start fraction, 3, divided by, 4, end fraction, start text, k, m, end text.

Hint #44 / 5

Let's find Julian's average speed.

$\begin{aligned} \text{speed} &=\dfrac{\text{distance}}{\text{time}}\\\\ &=\dfrac{2\dfrac{3}{4}\,\text{km}}{15\,\text{min}}\\\\ &=\dfrac{2\dfrac{3}{4}\,\text{km}}{15\,\cancel{\text{min}}}\times \dfrac{60\,\cancel{\text{min}}}{1\,\text{h}}\\\\ &=2\dfrac{3}{4}\times 4 \dfrac{\text{km}}{\text{h}}\\\\ &=11\,\dfrac{\text{km}}{\text{h}} \end{aligned}$

Hint #55 / 5

Julian has had an average speed of $11\dfrac{\text{km}}{\text{h}}$11, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction so far.