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)