Question

A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current.

Answer 1

Let x = speed of the current
then
(16-x) = speed upstream
and
(16+x) = speed downstream
:
Convert 20 min to hrs 20%2F60 = 1%2F3 hrs
Convert 15 min to hrs 15%2F60 = 1%2F4 hrs
:
Distance of the two trips is the same; write a dist equation: dist = time * speed
;
1%2F4(16+x) = 1%2F3(16-x)
Multiply both sides 12 to get rid of the denominators:
3(16 + x) = 4(16-x)
:
48 + 3x = 64 - 4x
:
3x + 4x = 64 - 48
:
7x = 16
x = 16%2F7
x ~ 2.3 mph is the current
:
Check solution with a calc, confirm that the distances are equal
.33*13.7 = 4.5
.25*18.3 = 4.5
: