Problema Solution
During the first part of a trip, a canoeist travels 24 miles
at a certain speed. The canoeist travels 7 miles on the second
part of the trip at a speed 5 mph slower. The total time
for the trip is 3 hours. What was the speed on each part of the
trip?
Answer provided by our tutors
let
v1 = the speed at the first part of the trip, v1>0
d1 = 27 miles the distance of the first part of the trip
v2 = the speed at the second part of the trip, V2>0
d2 = 7 miles the distance of the second part of the trip
on the second part of the trip the speed is 5 mph slower
v2 = v1 - 5
since speed = distance/time => time = distance/speed
total time of the trip is 3 hours
d1/v1 + d2/v2 = 3
27/v1 + 7/v2 = 3
by plugging v2 = v1 - 5 into the last equation we have
27/v1 + 7/(v1 - 5) = 3 multiply both sides by v1(v1 - 5)
27(v1 - 5) + 7*v1 = 3*v1*(v1 - 5)
by solving the equation we find two roots
first solution for v1
v1 = 12.8 mph
v2 = v1 - 5 = 7.8 mph
second solution for v1
v1 = 3.5 mph
v2 = 3.5 - 5 = -1.5 mph
since we assume that v2>0 this is not the solution of our problem
click here to see the step by step solution of the equation
the speed of the first part was 12.8 mph.
the speed of the second part was 7.8 mph.