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# Problem solving approach

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1. Hello

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

Thanks
2. 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
3. (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?
4. Daniel Atieh
This is relative motion.
Let be the velocity of the convoy and 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 and when the courier travels in the same direction the speed of the convoy relative to the courier is

Note:
is the speed of the convoy and is the speed of the courier.

In both instances one kilometre is travelled.

Hope this helps.
5. Hence we can deduce the following *in spoiler*
Spoiler:
Show

6. (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
7. (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.
8. 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!

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