Distance, Rate, and Time

Question

At noon one day, Corey decided to follow a straight course in a motor boat. After one hour of making no turns and traveling at a steady rate, the boat was 6 miles east and 8 miles north of its point of departure. What was Corey’s position at two o’clock?How far had Corey traveled? What was Corey’s speed?

 

Help would be appreciated. Thanks

Answer 1

Hi Gnarls,

 

You can think of the question as travelling in x and y coordinates versus crow fly. 6 and 8 refer to x and y coordinates and the straight course he travelled represents the crow fly distance. Does this remind you of a geometric shape? Yes, the right triangle with sides 6 and 8 miles. 

Then, according to the Pythagorean theorem, the distance he traveled is d² = 6² + 8²

d = 10 mi northeast of where he started 

He traveled this in one hour so his speed is 10 mi/hr

At two o'clock, he would have traveled 20 mi northeast of where he started.  

Answer 2

After one hour Corey had traveled along the hypotenuse of a right triangle North and East, hence he had traveled 

 

X² = (6² + 8²)^1/2  =(100)^1/2  = 10 miles in a somewhat North Easterly direction. (Pythagoras theorem)

 

At 2 o'clock two hours after he started Corey would have been 2*10 = 20 miles along in the same direction, ie 12 miles East and 16 miles North of his starting point.

 

his speed would have been 10/1 = 20/2 = 10 mph     (speed = distance covered/time taken)