The formula for finding the distance traveled, based on speed and time, is D=RTD=RT , whereD is distanceR is rate (speed) T is timeUnits must be consistent. If the unit for D is miles and the unit for T is minutes, what must the units for R be? Solve this formula for R.R = If a bicyclist rides for 160 minutes at an average speed of 17 miles per hour, how far was the ride, to 1 decimal place? miles.At what speed must a bicyclist ride to cover 12 miles in 1.5 hours, to 1 decimal place? miles/hour.

Answer and explanation:The formula for finding the distance traveled, based on speed and time, is [tex]D=R\times T[/tex]Where, D is distance , R is rate (speed)  and T is timeUnits must be consistent.1) Given : If the unit for D is miles and the unit for T is minutes.To find : What must the units for R be?Solution : [tex]R=\frac{D}{T}[/tex]Now we put unit,[tex]R=\frac{miles}{minutes}[/tex]The unit of R is miles per minute.2) Given : If a bicyclist rides for 160 minutes at an average speed of 17 miles per hour.To find : How far was the ride ?Solution : Speed R=17 miles per hourTime T=160 minutesConvert into hours,[tex]1\text{ minute}=\frac{1}{60}\text{ hour}[/tex][tex]160\text{ minute}=\frac{160}{60}\text{ hour}[/tex][tex]160\text{ minute}=2.67\text{ hour}[/tex]Substitute value in the formula,[tex]D=R\times T[/tex][tex]D=17\times 2.67[/tex][tex]D=45.39\text{ miles}[/tex]The distance is 45.4 miles.3) Given : A bicyclist ride to cover 12 miles in 1.5 hours.To find : At what speed must a bicyclist ride ?Solution : Distance D=12 milesTime T=1.5 hourSubstitute value in the formula,[tex]R=\frac{D}{T}[/tex][tex]R=\frac{12}{1.5}[/tex][tex]R=8[/tex]The speed is 8 miles per hour.