A boat takes 55 hours to go 20 miles upstream. It can go 50 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water. (Hint: Because the current pushes the boat when it is going downstream, the rate of the boat downstream is the sum of the rate of the boat and the rate of the current. The current slows down the boat when it is going upstream, so the rate of the boat upstream is the difference of the rate of the boat and the rate of the current.)

Question

Mathematics

Amaris Romero

2 August, 14:27

A boat takes 55 hours to go 20 miles upstream. It can go 50 miles downstream in the same time. Find the rate of the current and the rate of the boat in still water. (Hint: Because the current pushes the boat when it is going downstream, the rate of the boat downstream is the sum of the rate of the boat and the rate of the current. The current slows down the boat when it is going upstream, so the rate of the boat upstream is the difference of the rate of the boat and the rate of the current.)

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Brennen · Answer 1

We have two unknowns and two equations so we can solve this question.

The two unknowns are C (speed of current) and B (speed of boat)

Our boat traveled 20 miles in 55 hours going upstream which means it traveled. 36 miles in 1 hour; in other words. 36mph. Our boat traveled 50 miles in 55 hours going downstream; in other words. 909mph.

We can assume that because the boat managed to cover distance in the direction it was headed upstream it must have been going faster than the current so it moved at the speed of the boat minus the speed of the current and when it was going downstream it moved at the speed of the boat plus the speed of the current.

This gives us;

.36mph = B - C

.909mph = B + C

We solve for this system of equations and it simplifies to 1.27mph=2B

and B=.636mph

Plug this into one of the equations and we get that C=.2727mph

This means that the boat moved at. 363mph and the current moved at. 2727mph.