Hiker's rate is 6 mph, which is 3/11 of the bicycle's rate. how fast do they move towards each other? how fast do they get closer if the bicyclist catching up with the hiker? they move towards each other by the speed mph? if the bicyclist is catching the hiker, they get closer by the ?

They move towards each other by the speed 28 mph

If the bicyclist is catching the hiker, they get closer by the speed 16 mph

Step-by-step explanation:

Since, when two object are travelling in the opposite direction with the speed of x miles/h and y miles/h

Then, their relative speed = | x + y | miles/ h

While, when they are travelling in the same direction,

Then, their relative speed = | x - y | miles/h

Here, the hiker's rate = 6 miles/ h,

Also, 3/11 of the bicyclist's rate =  Hiker's rate

⇒ Bicyclist's rate = 11/3 of Hiker's rate = 11/3 × 6 = 22 miles/h

Hence, When, they move towards each other,

Their relative speed = 22 + 6 = 28 miles/h

While, If the bicyclist is catching the hiker,

That is, they are travelling in same direction,

Their relative speed = 22 - 6 = 15 miles/h