During the first 20 mile of a 50 mile bicycle race rogers average speed was 16mi/h. What must his average speed be during the remainder of the race if he is to finish the race in less than 2.5 h

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