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.

Answer 1

Answer: The rates of bicyclists of north and south are 20km/hr and 14km/hr respectively.

Explanation:

Since we have given that

Let the speed of bicyclist heading south be 'x'.

Let the speed of bicyclist heading north be 'x+6'.

Since they are moving in opposite directions,

So, relative speed = x+x+6=2x+6

Time taken = 10: 15 to 9:00 = 1 hour 15 minutes =
`1(15)/(60)=1(1)/(4)=(5)/(4)`

Distance between them = 42.5 km

According to question, it becomes,

`(Distance)/(time)=Speed\\\\(42.5)/((5)/(4))=2x+6\\\\42.5=(5)/(4)(2x+6)\\\\4* 42.5=5(2x+6)=10x+30\\\\170=10x+30\\\\170-30=10x\\\\140=10x\\\\x=(140)/(10)\\\\x=14\ km/hr`

Speed of bicyclist heading north would be 14+6=20 km/hr

So, the rates of bicyclists of north and south are 20km/hr and 14km/hr respectively.