I need help

Question

a motorboat can maintain a constant speed of 41 miles per hour relative to wate. The boat makes a trip upstream to a certain point in 42 minute; the return trip takes 40 minute. What is the speed of the the current?

Answer 1

in still water it goes 41 mph = 41/60 mile per minute

60 mph = 1 mile per minute

d=rt = distance = rate of speed times time

t =d/r

upstream takes 42 minutes = d/(b-c) = d/(41-c) = 42 where c= current speed

downstream takes 40 minutes = d/(b+c) = d/41+c) = 40

42(41-c) = d = 40(41+c)

42(41)- 42c = 40(41) + 40c

82c = 42(41)-40(41) = 2(41) = 82

c = 82/82 = 1 mph = current speed

d = 40(41+1)/60 = 40(42)/60 = 168/6 =84/3 = 28 miles downstream

d= 42(41-1)/60 = 42(40)/60 = 28 miles upstream

Answer 2

Hi Asia,

 

We will make use of the identity of distance to solve for the current speed.

The distance is the same going upstream and downstream, call it d.

d = speed * time

we can write

(41-x)*42/60 = (41+x)*40/60 (the left side of the equation is the distance going upstream and the right side is the distance going downstream)

If you solve for x, you should get 1 mph, the speed of the current.