Question

a boat takes two hours to travel 8km down and 8 km up the river when the water is till. How much time will the boat take to make the same trip when the river starts flowing at 4kmph?
1. 2 hours
2. 2 hour 40 minutes
3. 3 hours
4. 3 hour 40 minutes

Answer 1

Answer on Question #48625 – Physics – Mechanics | Kinematics | Dynamics

a boat takes two hours to travel 8km down and 8 km up the river when the water is till. How much time will the boat take to make the same trip when the river starts flowing at 4kmph?

1. 2 hours

2. 2 hour 40 minutes

3. 3 hours

4. 3 hour 40 minutes

Solution:

$S = 8km$ – travelled distance;

$t = 2hours$ – time to travel distance $S$ (when the water is till)

$v$ – velocity of the boat;

$u = 4\frac{km}{h}$ – velocity of the flow;

From the initial movement of the boat we can find it's velocity:

$$v = \frac{2S}{t} = \frac{v \cdot t}{2S} \quad (1)$$ $$v = \frac{2S}{t} = \frac{2 \cdot 8km}{2 \text{ hour}} = 8 \frac{km}{h}$$

Situation when the river starts to flow: time of the travel

$$T = t_{up} + t_{down}$$

Time to travel down the river:

$$t_{down} = \frac{S}{v + u} \quad (2)$$

Time to travel up the river:

$$t_{up} = \frac{S}{v - u} \quad (3)$$

(3) and (2) in (1):

$$T = \frac{S}{v + u} + \frac{S}{v - u} = S \left(\frac{1}{v + u} + \frac{1}{v - u}\right) = 8km \left(\frac{1}{8 \frac{km}{h} + 4 \frac{km}{h}} + \frac{1}{8 \frac{km}{h} - 4 \frac{km}{h}}\right) = 2.7 \text{ hours}$$

Answer: time to travel the same distance is equal to 2.7 hours.

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