Problem solving approach

DanielDaniels

14

Hello

any tips about how i can start this? or at least how i can visualise it?

Thanks

Reply 1

an_atheist

15

Half a minute to travel 1 km, how fast is that if the courier is the only thing moving?
3 minutes to travel 1 km, how fast is that if the courier is the only thing moving?
The average of these speeds will be the speed of the courier. I think

Reply 2

DanielDaniels

OP

14

Original post by an_atheist

Half a minute to travel 1 km, how fast is that if the courier is the only thing moving?
3 minutes to travel 1 km, how fast is that if the courier is the only thing moving?
The average of these speeds will be the speed of the courier. I think

Thank you for taking part.
it would lead to the answer, but didn't it say constant speed?
what do you think?

Reply 3

Cryptokyo

14

@Daniel Atieh
This is relative motion.
Let

v_{A}

be the velocity of the convoy and

v_{B}

the velocity of the courier.
When the couriers travels in the opposite direction to the convoy, the speed of the convoy relative to the courier is

|v_{A}|+|v_{B}|

and when the courier travels in the same direction the speed of the convoy relative to the courier is

|v_{B}|-|v_{A}|

Note:

|v_{A}|

is the speed of the convoy and

|v_{B}|

is the speed of the courier.

In both instances one kilometre is travelled.

Hope this helps.

(edited 7 years ago)

Reply 4

Cryptokyo

14

Hence we can deduce the following *in spoiler*

Spoiler

Reply 5

an_atheist

15

Original post by Daniel Atieh

Thank you for taking part.
it would lead to the answer, but didn't it say constant speed?
what do you think?

That's why you average.
It returns the same value as the previous poster
Or, he travels 2km in 3.5 minutes, find the speed from that

Reply 6

Cryptokyo

14

Original post by an_atheist

That's why you average.
It returns the same value as the previous poster
Or, he travels 2km in 3.5 minutes, find the speed from that

This method would give you an incorrect answer.

Reply 7

mik1a

10

The average method doesn't work for an interesting reason. Because the courier spends much longer catching up with the front of the convoy, he will be travelling at the slower speed (relative to the convoy) for a longer period of time. But when you average the two speeds, you're implicitly giving both legs an equal time-weighting.

E.g.1 I spend 1 hour walking at 2 mph, then I spend 1 hour running at 5 mph. Average speed = (2+5)/2. It is okay to average here because both speeds lasted the same amount of time.

E.g.2 I walk 1 mile at 2 mph, then run 1 mile at 5 mph. Average speed =/= (2+5)/2 ! It is not okay to average - even though the distance travelled is the same, the time spent doing each activity is not. Correct answer, work it out the long way: time spent walking = 0.5 hours; time spend running = 0.2 hours; total time spent = 0.7; average speed = total distance / total time = 2/0.7 = ~= 2.8 mph. Which is less than 3.5 mph (the average of 2 and 5).

Be wary of shortcuts!

(edited 7 years ago)

Problem solving approach

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you