Question

A boy can row a boat at a constant rate of 5 mi/hr in still water, as indicated in the figure. He rows upstream for 24 minutes and then rows downstream, returning to his starting point in another 16 minutes. (Round your answers to two decimal places.)

(A) Find rate of the current

(B) Find travel distance traveled

Answer 1

rate of current --- x mph

let the distance each way by y miles

so upstream distance:
y = (24/60)(5-x)
downstream distance
y = (16/60)(5+x)
but they are both equal to y, so

24(5-x)/60 = 16(5+x)/60
times 60
24(5-x) = 16(5+x)
120 - 24x = 80 + 16x
-40x = -40
x = 1

So the current is 1 mph
y = 16(6)/60 = 1.6 miles

(as a check sub in x = 1 into the other y = ... equation)

Answer 2

Two factory plants are making TV panels. Yesterday, Plant A produced
5000
fewer panels than Plant B did. Three percent of the panels from Plant A and
2%
of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced
750
defective panels?