School Certificate Maths Question (2 Viewers)

[mc1007]

Could someone please show me how to do this. I could guess the answer but I have no idea how to do it if I got another question similar:

72. Two Cars are travelling towards each other at 60 km/h and 80 km/h. How far apart are they 15 min before they pass each other

a) 5km
b) 9 1/3 km
c) 20 km
d) 35 km

 

[q3thefish]

Dash it bro.

 

[Schoey93]

Could someone please show me how to do this. I could guess the answer but I have no idea how to do it if I got another question similar:

72. Two Cars are travelling towards each other at 60 km/h and 80 km/h. How far apart are they 15 min before they pass each other

a) 5km
b) 9 1/3 km
c) 20 km
d) 35 km

Let the cars be A and B.
Let the amount of kilometres Car A (the slow car) is from Car B (the fast car) be x.

When Car A reaches Car B, x = 0.
When Car A is 15 km from Car B, naturally x = 15.
Total distance travelled 60 x 80 = 480 km (that's a multiplication sign, not a letter).
Divide 480 by 24 (because it took Car B 6 hours to make the trip and there are 4 lots of 6 hours in a day (6 x 4 = 24) ).
480/24 = 20 km

Therefore the cars are 20 km apart 15 min before they pass each other.

PS: There may be a flaw in my working; sorry. But hey, it got the right answer, didn't it?
You could probably graph an equation as an alternative method of solving this problem...

 

[annabackwards]

The car travelling at 60km/hr would be 15km (60/60 x 15) from the passing point.
The car travelling at 80km/hr would be 20km (80/60 x 15) from the passing point.

Therefore the distance is 15 + 20 = 35km
So D

 

[mc1007]

Thanks heeeeeps

 

[annabackwards]

Thanks heeeeeps

Just to clear things up, was the answer C or D?

If if the answer was D and you want a more detailed explanation, just ask

 

[Schoey93]

The car travelling at 60km/hr would be 15km (60/60 x 15) from the passing point.
The car travelling at 80km/hr would be 20km (80/60 x 15) from the passing point.

Therefore the distance is 15 + 20 = 35km
So D

Tell me, why did you add 15 and 20 instead of subtracting: 20 - 15?

Sorry; that was a really dumb question! 15 and 20 are both distances from the passing point, so to get the total distance you must add them together.

 

[annabackwards]

Tell me, why did you add 15 and 20 instead of subtracting: 20 - 15?

Sorry; that was a really dumb question! 15 and 20 are both distances from the passing point, so to get the total distance you must add them together.

Precisely

I assumed that they'd pass eachother at say point X and since you want the distance they were apart 15 min beforehand you work backwards.

Car A travelling at 60km/hr is say going left, so 15min before hand the car would be (60/60 x 15 as there are 60 mins in an hour) 15km to the left of X.

On the other handm, Car B travelling 80km/hr would be travelling right (in the opposite direction) and it'd be 80/60 x 15 = 20km to the right of X.

So all up it'd be 15+20 = 35km

 

[mc1007]

Yeah the answer was D 35kms.

Just wondering why you put the speeds over 60 mins eg (60/60 x 15)

Thanks again

 

[addikaye03]

Could someone please show me how to do this. I could guess the answer but I have no idea how to do it if I got another question similar:

72. Two Cars are travelling towards each other at 60 km/h and 80 km/h. How far apart are they 15 min before they pass each other

a) 5km
b) 9 1/3 km
c) 20 km
d) 35 km

You use vectors Vtotal=Va-(-Vb) So we set Vb to -Vb because it is going the opposite direction to Va

Since V=D/T so D=VT for a and b, now becareful because 15mins has to be converted to hrs to keep all the units right. So 0.25hrs

Da=60(0.25)=15km
Db=80(0.25)=20km

Therefore one travels 15km in one direction whilst the other travels 20km in opposite direction relative to a intersection point hence answer is D, 35km.

 

[Omnipotence]

Sigh, my method is easier.

1. 60km/1hr and 80km/hr
2. Ratio 60km:60min
3. Simplify, 1km:1min
4. Multiply by 45, 45km:45min
5. 80km - 45km = 35km
6. Answer D

 

[saberbladexx]

LOl the easiest method is
60/4=15
80/4=20
add them together and there you go.

@addikaye03:lol its year 10 maths.

 

[Amogh]

Yeah the answer was D 35kms.

Just wondering why you put the speeds over 60 mins eg (60/60 x 15)

Thanks again

we're converting 15 minutes to hours:
15/60 hours (which is 0.25)
then we're multiplying it to the speed 60 km/hr
and thus you get 15 km.
similarly you multiply 80*0.25 and get 20 km.
So the cars travelled 20 km and 15 km from the point of intersection..
distance between them is 35 km.

Let the cars be A and B.
Total distance travelled 60 x 80 = 480 km

how did you get that?

imo anna's method is the pro-est! w00t w00t!

 

[addikaye03]

@addikaye03:lol its year 10 maths.

lol yeah i know, but thats basically what i done, just explained why we add them since (Vt=Va-(Vb)) but i suppose that would look really odd to a yr 10 student

 

[Official]

Could someone please show me how to do this. I could guess the answer but I have no idea how to do it if I got another question similar:

72. Two Cars are travelling towards each other at 60 km/h and 80 km/h. How far apart are they 15 min before they pass each other

a) 5km
b) 9 1/3 km
c) 20 km
d) 35 km

140 (Car A + B) / 4 (15 mins = 1/4hr) = 35km.
No need for other bs =p

 

[duckcowhybrid]

You don't need to work it out, it's multiple choice. It can't be a since 5 is too small, can't be b because 9 and 1/3 is also too small, C doesnt work because 80/4 is already 20 so too small so it's gotta be D. You could do it in your head. It's SC Maths.

 

[addikaye03]

You don't need to work it out, it's multiple choice. It can't be a since 5 is too small, can't be b because 9 and 1/3 is also too small, C doesnt work because 80/4 is already 20 so too small so it's gotta be D. You could do it in your head. It's SC Maths.

Yeah i thought that too but he said what if i get a similar Q, ie. the possible answers may not make it so obvious next time, so that's why we provide a solution.