Relative Motion in One Dimension

Question 1:

A boat takes two hours to travel 4 km down and 4 km up the river when the water is still. How much time will the boat take to make the same trip when the river starts flowing at 2 kmph?

1. 2 hour

2. 2 hour 40 minute

3. 3 hour

4. 3 hour 40 minute

View Answer

Let the boat's speed in still water be x kmph. Given

$\frac{8}{x} = 2$

, we get x = 4 kmph.

With a 2 kmph current:

Downstream speed = 6 kmph, time = $\frac{4}{6} = \frac{2}{3}$

hours
Upstream speed = 2 kmph, time = $\frac{4}{2} = 2$

hours

Total time =

$2 \frac{2}{3}$

hours or 2 hours 40 minutes.

Question 2:

A taxi leaves the station X for station Y every 10 minutes. Simultaneously, a taxi leaves the station Y also for station X every 10 minutes. The taxis move at the same constant speed and go from X to Y or vice-versa in 2 hours. How many taxis coming from the other side will each taxi meet enroute from Y to X ?

1. 10

2. 11

3. 12

4. 23

View Answer

Each taxi takes 2 hours, and taxis leave every 10 minutes.

Taxis already on the route from X to Y:

$\frac{120}{10}$ $= 12$
Taxis that start after from X to Y:

$\frac{120}{10}$ $= 12$
Exclude the simultaneously departing taxi:

$12 + 11 = 23$

Final Answer: 23 taxis.