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.

Rates of two bicyclists are 18 km per hour and 14 km per hour.

Step-by-step explanation:

At 9:00 on Saturday morning, two bicyclists passes each other in opposite directions on a bicycle path.

Let the speed of a bicyclist heading north is = x km per hour

It is given that the speed of the bicyclist heading south is 4 km per hours less than the speed of the bicyclist heading north.

Therefore speed of bicyclist heading south will be = (x - 4) km per hour

After 1 hour and 15 minutes or 1.25 hours these bicyclists are 40 km apart.

Since distance = speed × time

So the equation will be

x(1.25) + (x - 4)(1.25) = 40

(1.25)(x - 4 + x) = 40

(1.25)(2x - 4) = 40

2x - 4 =

2x = 32 + 4

2x = 36

x = 18 km per hour will be the speed of the bicyclist heading north.

Speed of the bicyclist heading south = (x - 4) km per hour

                                                             = 18 - 4

                                                             = 14 km per hour

Therefore, rates of two bicyclists are 18 km per hour and 14 km per hour.

thats not a system of equations, that is a solution

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