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?

Question

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?

Elena Albarran · Accepted Answer

Sonya: #6.4# miles

Isaac: #5.4 # miles

#"distance" = "speed"xx"time"# Since the speeds are expressed in mph, the time must be expressed 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 Be mindful of the units: #mph xx h = m/cancelh xx cancelh# #=m# (miles)

Charles Aeschliman · Answer

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°# The separation between them: #d=sqrt(6.4^2+5.4^2) = sqrt70.12# #d~~8.4# miles

Nathan Ashcroft · Answer

undefined To find the distance each has traveled after 12 minutes, we first convert the time to hours since the speeds are given in miles per hour (mph).

12 minutes is 12/60 = 0.2 hours.

Sonya's distance traveled: 
Speed = 32 mph, Time = 0.2 hours
Distance = Speed × Time = 32 mph × 0.2 hours = 6.4 miles

Isaac's distance traveled:
Speed = 27 mph, Time = 0.2 hours
Distance = Speed × Time = 27 mph × 0.2 hours = 5.4 miles

Therefore, Sonya has traveled 6.4 miles, and Isaac has traveled 5.4 miles.