5.) A boat makes a trip downstream in 5 hours. The return trip against the current takes 12 hours. If the speed of the current is 3 1/2 km/h, what is the speed of the boat in still water?

6.) How far does the boat referred to in Exercise 5 travel (one-way)?

The boat travels downstream at the rate of r+3.5 and r-3.5 upstream.

distance down stream = r*time = (r+3.5)*5 and upstream is (r-3.5)*12.
Since the distance downstream is the same as distance upstream, these two are equal to each other.
(r+3.5)*5 = (r-3.5)*12
Solve for rate of the boat in still water.
That should help you solve b part.

To solve both questions 5 and 6, we need to use the concept of relative velocity.

Let's assume the speed of the boat in still water as "B" km/h.

In question 5, we are given that the boat makes a trip downstream in 5 hours. This means it is going with the current, so the effective speed will be the sum of the speed of the boat in still water (B) and the speed of the current (3 1/2 km/h).

So, the speed downstream is B + 3 1/2 km/h. The time taken downstream is 5 hours.

On the return trip, the boat is going against the current, which reduces its effective speed. So, the speed upstream is B - 3 1/2 km/h. The time taken upstream is 12 hours.

Now, we can use the formula: Distance = Speed × Time

For the downstream trip:
Distance downstream = (B + 3 1/2) km/h × 5 hours

For the upstream trip:
Distance upstream = (B - 3 1/2) km/h × 12 hours

Since the distances of the downstream and upstream trips are equal (as it is a round trip), we can set these two distances equal to each other and solve for B.

(B + 3 1/2) km/h × 5 hours = (B - 3 1/2) km/h × 12 hours

Now, let's solve this equation step by step:

5B + 17.5 = 12B - 42

Collecting like terms:

7B = 59.5

Dividing both sides of the equation by 7:

B = 8.5 km/h

So, the speed of the boat in still water is 8.5 km/h.

Now, let's move on to question 6. We need to find the distance traveled by the boat for a one-way trip.

For the downstream trip:
Distance downstream = (8.5 km/h + 3 1/2 km/h) × 5 hours

Distance downstream = 12 km/h × 5 hours

Distance downstream = 60 km

Therefore, the boat referred to in exercise 5 will travel 60 km for a one-way trip.