Word problem help? 2

Question

Two boats travel at right angles to each other after leaving the same dock at the same time. One hour later, the boats are 5 miles apart. If one boat travels 1 mile per hour faster than the other boat, find the rate of each boat.

 

 

The rates of the two boats are ___

Answer 1

the distances the boats travel and the 5 mile distance form a right triangle

the 5 mile distance is the hypotenuse

distance=rate*time

time=1 (hour)

therefore distance=rate

the fact that one rate is 1 mile per hour faster than the other rate and the hypotenuse is 5 miles tells me you have a 3-4-5 right triangle; 5, r+1, and r where r=3 and r+1=4

solving algebraically...

d=r*t where t=1 and one rate is r and the other rate is r+1

using the Pythagorean Theorem

5²=r²+(r+1)²

25=r²+r²+2r+1

2r²+2r+1-25=0

2r²+2r-24=0

divide both sides by 2

r²+r-12=0

factor

(r+4)(r-3)=0

r-3=0

r=3 mph

r+1=4 mph