Noah is trying to qualify for a race. a driver needs to complete 8 laps of a seven-mile track at an average speed of 105.66 mph to qualify. noah has already completed the first three laps. his average speed so far is ninety-two mph. what must his average speed be for the rest of the race to qualify? a) approximately 146 mph b) approximately 96 mph c) approximately 116 mph d) approximately 136 mph e) approximately 106 mph f) approximately 126 mph

C) Approximately 116 mph

Step-by-step explanation:

The total race is (8 laps)·(7 mi/lap) = 56 miles. Noah has completed 3 laps, or 21 miles, and has 35 miles to go.

The total time allowed for qualification is a maximum of ...

... 56 miles/(105.66 mph) ≈ 0.530002 . . . hours

The time Noah has used so far is ...

... 21 miles/(92 mph) ≈ 0.228261 . . . hours

so he is allowed

... 0.530002 -0.228261 = 0.301741 . . . hours

to finish the last 35 miles.

This requires him to have an average speed of ...

... 35 miles/(0.301741 hours) = 115.993 miles/hour

Noah's average speed must be approximately 116 mph for the rest of the race to qualify.