Problema Solution
A motorboat on a river maintained a constant speed of 10 mph relative to the water. The boat is traveling 9 miles upstream and then returning the 9 miles downstream. The total time for the trip is 5.0 hours. Find the speed of the current, assuming it is a constant rate.
a) What will the variable you use represent? Included units:
b)As you go upstream, if the boat is traveling at 10 mph and the river has a current of x mph what is the actual rate of the boat as it goes upstream?
c) As you go downstream, if the boat is traveling at 10 mph and the river has a current of x mph, what is that actual rate of the boat as it goes downstream?
Answer provided by our tutors
let x = the speed of the current
since speed = distance/time => time = distance / speed
the time going upstream + the time going downstream = 5 hours
9/(10 + x) + 9/(10 - x) = 5 multiply both sides by (10 - x)(19 + x)
9(10 - x) + 9 (10 + x) = 5 (x + 10)(x - 10)
5x^2 - 500 = 180
x^2 = 680/5
x^2 = 136
x = 2 * (34^0.5)
x = 11.66 mph approximately
the speed of the current is 11.66 mph approximately.
a) What will the variable you use represent? Included units:
x = mph the speed of the current
b)As you go upstream, if the boat is traveling at 10 mph and the river has a current of x mph what is the actual rate of the boat as it goes upstream?
(10 - x) mph
c) As you go downstream, if the boat is traveling at 10 mph and the river has a current of x mph, what is that actual rate of the boat as it goes downstream?
(10 + x) mph