SOLUTION: In calm water, a motorboat can travel five times as fast as the current in the Amazon River. A trip upriver (upstream) and back totaling 96 km takes 5 hrs. Find the rate of the cur

Algebra ->  Rate-of-work-word-problems -> SOLUTION: In calm water, a motorboat can travel five times as fast as the current in the Amazon River. A trip upriver (upstream) and back totaling 96 km takes 5 hrs. Find the rate of the cur      Log On


   

Question 1197751: In calm water, a motorboat can travel five times as fast as the current in the Amazon River. A trip upriver (upstream) and back totaling 96 km takes 5 hrs. Find the rate of the current.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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In calm water, a motorboat can travel five times as fast as the current in the Amazon River.
A trip upriver (upstream) and back totaling 96 km takes 5 hrs. Find the rate of the current.
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Let x be the rate of the current in the river, in km/h.

Then the rate of the motorboat at calm water is 5x km/h;

the effective rate traveling downstream is 5x+x = 6x km/h;
the effective rate traveling   upstream is 5x-x = 4x km/h.


The total round trip is 96 km; hence, one way (each way) trip is 48 km.


Time equation is

    48%2F%284x%29 + 48%2F%286x%29 = 5  hours.    (1)


Cancel common factors

    12%2Fx + 8%2Fx = 5


Simplify and find x

    20%2Fx = 5

     x = 20%2F5 = 4 km/h.


ANSWER.  The rate of the current is 4 km/h.


CHECK.  We will check equation (1):  48%2F%284%2A4%29 + 48%2F%286%2A4%29 = 48%2F16 + 48%2F24 = 3 + 2 = 5 hours.   ! correct !

Solved.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let the speed of the current be x; then the speed of the motorboat in calm water is 5x. The upstream and downstream speeds of the boat on the river are then 4x and 6x.

The ratio of the upstream and downstream speeds is 4x:6x = 2:3; the distance upstream and downstream are the same. That means the ratio of times for the upstream and downstream trips is 3:2.

The total trip takes 5 hours, so the upstream time is 3 hours and the downstream time is 2 hours.

The round trip is 96km, so each leg is 48km.

48km upstream in 3 hours means the upstream speed is 16km/hr. But the upstream speed is 4x, so x = 4.

ANSWER: The speed of the current is x = 4km/hr.