Two boats travel at right angles to each other after leaving the same dock at the same time. 1 hour later they are 5 miles apart. If one travels 1 miles faster than the other, what is the rate of each?

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Answer 1 · 2017-02-16T09:27:14

Faster boat: 4 miles/hr; Slower boat: 3 miles/hr

Let the slower boat travel at #x# miles/hr

#:. # the faster boat travels at #(x+1)# miles/hr

After 1 hour the slower boat has travelled #x# miles
and the faster boat has travelled #x+1# miles.

We are told that:
(i) the boats travel at right angles to each other and
(ii) after 1 hour the boats are 5 miles apart

Hence we can use Pythagoras on the right angle triangle formed by the path of both boats and the distance between them as follows:

#x^2 +(x+1)^2 = 5^2#

#x^2 + x^2 +2x+1 = 25#

#2x^2 +2x -24 = 0#

#x^2 +x -12 =0#

#(x+4)(x-3)=0#

Since: #x>0 -> x=3#

#:.# The faster boat travels at #(3+1)= 4# miles/hr; The slower boat travels at 3 miles/hr.