Question

a 4 hr river cruise goes 20 km upstream and then back again. the river has a current of 3 km an hr going downstream. what is the boat's speed in still water and how long was the upstream journey in minutes? round to the nearest tenth for each

Answer 1

I think that, during the upstream journey, the relative speed boat with respect to the riverbank is v+3, where v is the speed of the boat with respect to the water.
so time employed by the boat to make the upstream journey, is:
\[\frac{ d }{ v+3 }\]
where d= 20Km

Answer 2

during the downstream journey, our boat has relative speed v-3, with respect to the riverbank, so the time employed by our boat to make the downstream journey, is:
\[\frac{ d }{ v-3 }\]

Answer 3

now, if we add both times each other, we can get this:
\[\frac{ d }{ v+3 }+\frac{ d }{ v-3 }=4\]
substituting for d, we have:
\[\frac{ 20 }{ v+3 }+\frac{ 20 }{ v-3 }=4\]

Answer 4

please note that the above is a quadratic equation.
Solving for v, we get two solutions, even if only one of them is acceptable.
Our acceptable solution is:
\[v=5+\sqrt{34}=10.8 Km/hour\]

Answer 5

so time employed by the boat for upstream journey, is:
\[\frac{ 20 }{ 10.8+3 }=...\]
please, complete the computation

Answer 6

if something is not clear, please tell me!

Answer 7

1.5 hrs?

Answer 8

better is 1.4 hrs