Amotor scooter travels 20 mi in the same time that a bicycle covers 8 mi if the rate of the scooter is 4 mph more than twice the rate of the bicycle, find both rates

We observe that 20 is 4 more than twice 8. This suggests the time is 1 hour and the rates are

... scooter: 20 mi/h

... bicycle: 8 mi/h

You can let b represent the rate of the bicycle in miles per hour. Then we have (for time in hours and distance in miles) ...

... time = distance/speed

... time = 20/(2b+4) = 8/b

... 20b = 8(2b+4) = 16b +32

... 4b = 32

... b = 8

The rate of the bicycle is 8 mph; that of the scooter is 2*8+4 = 20 mph.

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.