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# Word problem help? 2

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 ___

### 1 Answer by Expert Tutors

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
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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