Answer:
His average speed has to be greater than 24 miles per hour to finish the race in less than 2.5 h
Step-by-step explanation:
Step 1
Determine the expression for calculating the speed, distance and time as follows;
D=S×T
where;
D=distance covered in miles
S=speed in miles per hour
T=time in hours
Step 2
Using the expression above, determine the time taken to travel 20 miles as shown;
Rearranging the expression;
T=D/S
where;
D=20 miles
S=16 miles/hour
replacing;
T=(20/16)=1.25 hours
Step 3
The expression for the remaining time you need to take to finish the rate in less than 2.5 h
remaining time=(2.5 h-1.25 h)=1.25 h
The remaining time has to be less than 1.25 h
Step 4
Determine the expression for calculating the remaining distance to be covered as follows;
Remaining distance=Total distance-distance traveled
where;
Total distance=50 miles
distance traveled=20 miles
replacing;
Remaining distance=(50-20)=30 miles
Step 3
Rogers average speed has to be expressed as shown to finish in less than 2.5 h
Average speed>remaining distance/remaining time
where;
remaining distance=30 miles
remaining tile=1.25 h
replacing;
Average speed>(30/1.25)=24 miles per hour
His average speed has to be greater than 24 miles per hour to finish the race in less than 2.5 h
