A boat is traveling in a river with a current that has a speed of 1.5 km/h. In one hour, the boat can travel twice the distance downstream as it can travel upstream. How long will it take the boat to travel 100 km in still water?

If the still-water speed is s, then since distance = speed*time, then in equal time (say, t=1),

(s+1.5) = 2(s-1.5)
s+1.5 = 2s-3
s = 4.5

100/4.5 = 22.22 hrs
or 22 hr 13 min 20 sec

Well, if the boat can travel twice the distance downstream as it can travel upstream, then I guess it really enjoys going with the flow! Talk about going with the current!

Now, let's unravel this mystery. Let's say the speed of the boat in still water is "B" km/h, and the speed of the current is 1.5 km/h.

When the boat is going downstream, its effective speed is the sum of the speed of the boat in still water and the speed of the current. So, the effective speed is B + 1.5 km/h.

When the boat is going upstream, its effective speed is the difference between the speed of the boat in still water and the speed of the current. So, the effective speed is B - 1.5 km/h.

Now, if the boat can travel twice the distance downstream as it can travel upstream, we have the equation:

(B + 1.5) × 2 = (B - 1.5) × 1

Let's solve this equation for B, the speed of the boat in still water. *Clown-bot activates brain circuits...beep boop*

2B + 3 = B - 1.5

B = -4.5

Wait a minute! Negative speed? That can't be right! *Clown-bot scratches head*

Let's rewind and start over.

Now, we want to know how long it will take for the boat to travel 100 km in still water. Let's say t is the time it takes in hours.

Going downstream, the boat will cover 100 km in t hours while benefiting from the current:

100 = (B + 1.5) × t

And going upstream, the boat will cover 100 km, but at a slower pace:

100 = (B - 1.5) × t

Dividing both equations, we get:

(B + 1.5) × t / ((B - 1.5) × t) = 1

Simplify, simplify, simplify:

(B + 1.5) / (B - 1.5) = 1

Cross-multiplying:

B + 1.5 = B - 1.5

Hmm... that's strange, it seems like the equation can't be solved. Well, it looks like this boat trip has received a visit from the Bermuda Triangle of math problems! My apologies for not reaching a definitive answer. Better luck next time!

To solve this problem, we can use the concept of relative velocity.

Let the speed of the boat in still water be V km/h, and let the speed of the current be 1.5 km/h.

When the boat is traveling downstream, its effective speed will be V + 1.5 km/h, as it is moving in the same direction as the current.

When the boat is traveling upstream, its effective speed will be V - 1.5 km/h, as it is moving against the current.

We are given that the boat can travel twice the distance downstream than upstream in one hour. This means that if the boat's speed in still water is V km/h, it will travel V + 1.5 km downstream in one hour and V - 1.5 km upstream in one hour.

As per the given information, the boat traveled twice as far downstream as upstream, so we can set up the following equation:

V + 1.5 = 2(V - 1.5)

Simplifying the equation:

V + 1.5 = 2V - 3

3 + 1.5 = 2V - V

4.5 = V

So, the speed of the boat in still water is 4.5 km/h.

Now that we know the speed of the boat in still water, we can calculate the time it takes to travel 100 km using the formula:

Time = Distance / Speed

Time = 100 km / 4.5 km/h

Time = 22.22 hours (rounded to 2 decimal places)

Therefore, it will take approximately 22.22 hours for the boat to travel 100 km in still water.

To solve this problem, let's break it down step by step:

Let's start by assuming the speed of the boat in still water is "x" km/h.

When the boat is traveling downstream, it moves with the current, which adds another 1.5 km/h to its speed. So the effective speed downstream is (x + 1.5) km/h.

Similarly, when the boat is traveling upstream, it moves against the current, which subtracts 1.5 km/h from its speed. So the effective speed upstream is (x - 1.5) km/h.

Given the condition that the boat can travel twice the distance downstream as it can travel upstream in one hour, we can write the equation:

(x + 1.5) = 2(x - 1.5)

Now, let's solve this equation to find the value of x:

x + 1.5 = 2x - 3
3 + 1.5 = 2x - x
4.5 = x

Therefore, the speed of the boat in still water is 4.5 km/h.

Now, let's find the time it will take for the boat to travel 100 km in still water:

To calculate this, we need to find the time for the boat to travel 100 km downstream and upstream separately.

Downstream:
Time = Distance / Speed
Time = 100 km / (4.5 km/h + 1.5 km/h) = 100 km / 6 km/h = 16.67 hours

Upstream:
Time = Distance / Speed
Time = 100 km / (4.5 km/h - 1.5 km/h) = 100 km / 3 km/h = 33.33 hours

To find the total time taken, we need to add the time taken downstream and the time taken upstream.

Total Time = Time Downstream + Time Upstream
Total Time = 16.67 hours + 33.33 hours = 50 hours

Therefore, it will take the boat 50 hours to travel 100 km in still water.