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

Answer 1

Answer:

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 = $\frac{40}{1.25}=32$

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.

Answer 2

Let x be the rate of the slower bicyclist and
      x + 4 be the rate of the faster bicyclist

Since the bicyclists are headed towards opposite directions, the sum of the distances they covered traveling for one hour and 15 minutes should be equal to 40 km based on the given conditions above. This may be expressed as,
 
                                   (x)(1.25) + (x + 4)(1.25) = 40

Calculating gives x = 14 

Thus, the rate of the bicyclists are 14 km/h and 18 km/h.