Rates of two bicyclists are 18 km per hour and 14 km per hour.
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.
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northbound bicyclist is going 15 km/h and the southbound bicyclist is going 11 km/h
(A)northbound bicyclist = 15 km/h; southbound bicyclist = 11 km/h
Let the speed of the bicycle that is going to the south = x km/h
Thus, according to the question,
The speed of north going bicycle = ( x + 4 ) km/h
Since, they are going opposite to each other,
Hence, the relative speed of the both bicycle = (x + x + 4) km/h = (2 x+ 4) km/h
Now, after crossing each other at 10:30 AM, they are 39 km apart.
⇒ Relative distance = 39 km,
And, the relative time = 1 hour 30 minutes = hours = 3/2 hours,
Therefore, the speed of south going bicycle = x km/h = 11 km/h
And, the speed of north going bicycle = (x + 4) km/h = 15 km/h