. At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 6 km/hour faster than the bicyclist heading south. At 10:15, they are 42.5 km apart. Find the two bicyclists’ rates.

Question

.  At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 6 km/hour faster than the bicyclist heading south. At 10:15, they are 42.5 km apart. Find the two bicyclists’ rates.

anonymous · Answer

@eSpeX i need help lol

espex · Answer

You have two people traveling, the distance that each of them traveled totals 42.5km.
Traveler A is going xkm/hr for 1.25hrs, traveler B is going 6*xkm/hr for 1.25hrs, this produces the following formula:$$6x*1.25 + x*1.25 = 42.5$$ working this out we get $$7.5x + 1.25x = 42.5 \rightarrow 8.75x=42.5 \rightarrow x=4.86\frac{km}{hr}$$

So traveler A is moving 4.86km/hr
traveler B is moving 6 * 4.86 --> 29.16km/hr

anonymous · Answer

see on the multiple choice it says a) northbound bicyclist 20km/h southbound bicyclist 14 k/h 
b)north 23km/h south 17 km/h
c)north 18km/h south 11km/h
d)north 20km/h south 13km/h

espex · Answer

Well given they traveled a collective speed of 34km/hr I would say that it was A.
If you go 42.5km/1.25hrs = 34km/hr and A is the only one that totals 34.

espex · Answer

Duh... Okay I see what I did wrong and I feel silly.

espex · Answer

Traveler A and traveler B collectively went 42.5km in 1.25hrs. Algebraically that is:
1.25(x + (x+6))=42.5  (Notice it's + and not *)
1.25x + 1.25x + 7.5 = 42.5
2.5x + 7.5 = 42.5
2.5x = 35
x = 14

So, traveler A is going 14km/hr
traveler B is going 6km + 14km = 20km/hr.