Solve Distance Problem: Boy Riding Bicycle for 30km

[Equilibrium]

Homework Statement

This problem has already been solved but i got a quite few clarifications:
http://www.algebra.com/algebra/homework/word/travel/Travel_Word_Problems.faq.question.493396.html

"a boy on his bicycle intends to arrive at a certain time to a town that is 30 km away from his home .after riding 10 km, he rested for half an hour and as a result he was obliged to ride the rest of the trip 2km/hr faster ."

Homework Equations

v = d/t
t = d/v

The Attempt at a Solution

Why did he disregard the 10km?
i think the formula should've of look like this:
$$\frac{30}{s}=\frac{10}{s}+0.5+\frac{20}{s+2}$$
(total time riding on original speed for the whole trip) = (time riding on original speed (for 10km))+(time rested)+(faster velocity on the rest (for 20km))

the formula he used:
$$\frac{30}{s}=\frac{30}{s+2}+0.5$$

 

[Simon Bridge]

He has to go 20km in the time remaining after traveling 10km at the slow speed, and waiting half an hour.

The time remaining is $20/s = 0.5 + 20/(s+2)$ ... agreeing with your formulation.

$40(s+2) = (s+2)s + 40s$

rearranging:
$s^2+2s-80=0$

by quadratic equation:
$s \in \{ 10,-8 \}$

possible answers are 10hr and -8hr ... pick the positive one.
This is the same answer.

So your question is, "how did he know that his version would be correct?"
Try plotting the velocity-time graph.

 

[nasu]

The solutions to the quadratic equation are +8 and -10.
The solution for the problem is then 8km/h.

In the link given he is solving a different problem. I suppose he did not read the problem carefully.

 

[Simon Bridge]

Did I set up the quadratic incorrectly ...

the discriminant is 324
so $s =\frac{1}{2}(-2\pm\sqrt{324}=1\pm 9$ ... Oh I see: I misplaced a minus sign!
<mumble mumble grzzl>
... time for bed!

 

[Nickie]

(distance of whole trip divided by original speed) = (distance of whole trip divided by faster speed)+(time rested)

I would approach this problem by first understanding the given information and identifying any inconsistencies or potential errors. In this case, it seems that the formula used by the person who solved the problem may not fully reflect the scenario described.

Based on the problem statement, the boy rode for 10km at a certain speed, then rested for half an hour, and then rode the remaining 20km at a speed that was 2km/hr faster. The formula used by the person who solved the problem only takes into account the time rested and the faster speed for the remaining 20km, but does not account for the initial 10km that the boy rode.

Therefore, I would use the formula that you suggested, which takes into account the time for the entire trip and the two different speeds used. This would provide a more accurate representation of the scenario and would give a more precise solution. I would also double check the given information and make sure that it is consistent and accurate.

In addition, as a scientist, I would also consider other factors that may affect the boy's speed, such as terrain, weather conditions, and whether the boy is riding alone or with a group. These factors could impact the overall time and speed of the trip and should be taken into account when solving the problem.