Algebra and Please help .

Question

A motor scooter travels 1616 mi in the same time that a bicycle covers 77 mi. If the rate of the scooter is 55 mph more than twice the rate of the? bicycle, find both rates

Answer 1

The distance formula is   d = rt

distance = rate*time

 

This can be rewritten to solve for time

t = d/r

 

Let r = rate of the bicycle

rate of motor scooter = 2r + 55

 

Bicycle:  t = 77/r

 

Motorscooter:  t = 1616/(2r+55)

 

The times are the same so:

 

77/r = 1616/(2r+55)   cross multiply

1616r = 77(2r+55)

1616r = 154r + 4235  subtract 154r from both sides

1462r = 4235             divide both sides by 1462

r = 4235/1462

r = 2.9 mph

 

The bicycle travelled at 2.9 mph

The motorscooter travelled at 2r+55 = 2(2.9)+55 = 60.8 mph

 

Note:  This was done with rounding since the rate of the bicycle was

          2.89672 mph