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?

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Answer 1 · 2017-07-07T07:29:54

They have travelled $6.4 and 5.4$ miles resp

and are then $8.4$ miles apart.

First find the distance travelled Sonya in $12$ minutes

$32*12*1/60=6.4$ miles from the centre of the lake.

Then find the distance travelled by Isaac in $12$ minutes
$27*12*1/60=5.4$ 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:

$d=sqrt(6.4^2+5.4^2) = sqrt70.12$

$d~~8.4$ miles

Answer 2 · 2017-07-07T07:41:42

Sonya: $6.4$ miles

Isaac: $5.4$ miles

$"distance" = "speed"xx"time"$

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

$12 min = 12/60 hour = 1/5 hour$

**Sonya: **
$"distance" = 32mphxx1/5 h$

$= 6 2/5 = 6.4$ miles

Isaac:
$"distance" = 27mphxx1/5 h$

$= 5 2/5 = 5.4$ miles

Take note of the units:

$mph xx h = m/cancelh xx cancelh$

$=m$ (miles)