221k views
2 votes
A motorboat can maintain a constant speed of 41 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 43 ​minutes; the return trip takes 39 minutes. What is the speed of the​ current?

User Quark Soup
by
8.5k points

1 Answer

0 votes

Answer:

speed of current = 2.1 mph

Explanation:

Let the speed of the current be "c" and the speed of the motorboat in still water be "b".

We know that the boat can maintain a constant speed of 41 miles per hour relative to the water. Therefore, the speed of the boat upstream would be:

b - c = 41 mph

Similarly, the speed of the boat downstream would be:

b + c = 41 mph (since the boat maintains the same speed relative to the water)

Now, we need to use the given times to form equations that relate the distance traveled and the speed. Let the distance to the point be "d".

Upstream:

distance = speed x time

d = (b - c) x (43/60)

Downstream:

distance = speed x time

d = (b + c) x (39/60)

Since the distance traveled in both cases is the same, we can equate the two expressions:

(b - c) x (43/60) = (b + c) x (39/60)

Multiplying both sides by 60/3 gives:

(b - c) x 43 = (b + c) x 39

Expanding both sides gives:

43b - 43c = 39b + 39c

Simplifying:

4b = 82c

b = 20.5c

Substituting this into the first equation we obtained:

b - c = 41

20.5c - c = 41

19.5c = 41

c = 2.1 mph (rounded to one decimal place)

Therefore, the speed of the current is 2.1 mph.

User Poger
by
8.1k points