Question

a motorboat can mjaintain a constant speed of 26 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 17 mintues; the return trip takes 9 mintues what is the speed of the current

Answer 1

let v_c be the speed of current and x be the distrance travelled in the trip to a certain point. When the boat was travelling upstream, its speed was slower than the speed during the return trip of the same distance. So that means that, when it was going upstream, the total speed of the boat is the difference of its own speed and the speed of the current and when it was returning, it was going with the flow of the current which is why it was faster. So its speed upon returning is the sum of the speed of the boat and the speed of current.
we know that the distance x travelled during the trip and the return trip are the same and that vt=d, so we'll come up with,
(26 miles/hr - v_c)17 min=x
(26 miles/hr +v_c)9 min =x
so
(26 miles/hr - v_c)17 min=(26 miles/hr +v_c)9 min
now we can solve for v_c...

Answer 2

what would we do with 17
and 9

Answer 3

you could divide both sides with 9 min and end up with
(26 miles/hr - v_c)17/9=26 miles/hr +v_c
(17/9)(26 miles/hr)-(17/9)v_c=26 miles/hr +v_c
(17/9)(26 miles/hr)-26 miles/hr=(17/9)v_c+v_c
26 miles/hr((17/9)-1)=v_c((17/9)+1)
((26 miles/hr)((17/9)-1))/((17/9)+1)=v_c