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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 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.

Guest Jul 18, 2017
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After they pass at 9PM, they continue traveling for 1.25 hours

 

So...let the rate of the slower cyclist = R and the faster R + 4

 

And rate * time  =  total distance

 

So.....

 

Distance traveled by slower cyclist after passing + Distance traveled by faster cyclist after passing = 40 km

 

So....

 

R * 1.25 + (R + 4) * 1.25  =  40   simplify

 

1.25R + 1.25R + 5 = 40  

 

2.50R  + 5  =  40     subtract 5 from both sides

 

2.50R = 35      divide both sides by 2.50

 

R = 14 k/ hr    =  rate of slower cyclist

 

And R + 4  = 18 km/ hr  =  rate of faster cyclist 

 

 

cool cool cool

CPhill  Jul 18, 2017

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