what is the speed of the current?

Question

A motorboat can maintain a constant speed of

12 miles

per hour relative to the water. The boat makes a trip upstream to a certain point in

60 minutes

​ the return trip takes

36 minutes

What is the speed of the​ current?

Answer 1

I think what this problem means is this:

w=speed of the current

upstream (against the current) distance: (w-12)*60

downstream (with the current) distance: (w+12)*36

60(w-12)=36(w+12)

divide by 6

10w-120=6w+72

4w=192

w=12 (mph)

Answer 2

The distance up steam and down stream are equal. The current speed is equal in both directions but opposite. The up steam rate is 12 miles/hours - Current miles/ hour and the down steam is 12 miles/hour + Current miles/hour. The times must be converted into hours since the speeds are in hours. 60 minutes = 1 hour and 36 minutes = 36 /60 or 0.6 hours. The equality becomes: 1 (12- C) = 0.6 ( 12 + C).

Multiplying through: 12 - C = 7.2 + C

Add C to both sides: 12 = 7.2 + 2 C

Subtract 7.2 from both sides: 4.8 = 2 C

Divide by 2: 2.4 miles/ hour = C