Answer:
The maximum speed of bicycle and scooter are 30 miles/hour and 40 miles/hour respectively.
Step-by-step explanation:
Let the speed of electric bicycle be x
We are given that A scooter travels 10 miles per hour faster than an electric bicycle.
So, Speed of scooter = x+10
The scooter traveled for 3 hours
The bicycle traveled for [tex]5\frac{1}{2}=5.5 hours[/tex]
Distance traveled by scooter =[tex]Time \times Speed = 3(x+10)=3x+30[/tex]
Distance traveled by bicycle =5.5x
We are given that All together the scooter and bicycle traveled no more than 285 miles
So, [tex]3x+30+5.5x \leq 285[/tex]
[tex]8.5x+30\leq 285[/tex]
[tex]8.5 x \leq 285-30[/tex]
[tex]8.5 x \leq 255[/tex]
[tex]x\leq \frac{225}{8.5}[/tex]
[tex]x\leq 30[/tex]
Maximum speed of bicycle = 30 miles/hour
Maximum speed of scooter = x+10=30+10=40 miles/hour
Hence the maximum speed of bicycle and scooter are 30 miles/hour and 40 miles/hour respectively.
