# Sonya and Isaac are in motorboats located at the center of a lake. At time t = 0, Sonya begins traveling south at a speed of 32 mph. At the same time Isaac takes off, heading east at 27 mph. How far have they traveled after 12 minutes?

Jul 7, 2017

They have travelled $6.4 \mathmr{and} 5.4$ miles resp

and are then $8.4$ miles apart.

#### Explanation:

First find the distance travelled Sonya in $12$ minutes

$32 \cdot 12 \cdot \frac{1}{60} = 6.4$ miles from the centre of the lake.

Then find the distance travelled by Isaac in $12$ minutes
$27 \cdot 12 \cdot \frac{1}{60} = 5.4$ miles from the centre of the lake

To find the distance between Sonya and Isaac, we can apply the Pythagorean theorem as the angle between them is 90°

Distance between them:

$d = \sqrt{{6.4}^{2} + {5.4}^{2}} = \sqrt{70.12}$

$d \approx 8.4$ miles

Jul 7, 2017

Sonya: $6.4$ miles

Isaac: $5.4$ miles

#### Explanation:

$\text{distance" = "speed"xx"time}$

The speeds are given in mph so the time needs to be in hours.

$12 \min = \frac{12}{60} h o u r = \frac{1}{5} h o u r$

Sonya:
$\text{distance} = 32 m p h \times \frac{1}{5} h$

$= 6 \frac{2}{5} = 6.4$ miles

Isaac:
$\text{distance} = 27 m p h \times \frac{1}{5} h$

$= 5 \frac{2}{5} = 5.4$ miles

Take note of the units:

$m p h \times h = \frac{m}{\cancel{h}} \times \cancel{h}$

$= m$ (miles)