To qualify for the race, each driver must complete 2 laps of the track at an average speed of 100 mi/h. Benjamin averages only 75 mi/h on his first lap. How fast must he go on his second lap to qulify for the race?

let the distance around the track be d km

so the time needed to qualify is 2d/100

his time for the first lap is d/75 hours
let his speed for the second lap be r km/h
so the time for his second lap is d/r hours

total time = d/75 + d/r = (dr+75d)/75

then (dr+75d)/75 = 2d/100

divide both sides by d
(r+75)/75 = 2/100

you finish it, let me know what you got

i got 3675, but that doesn't make any sense, he has to go 3675 mph?

I believe Reiny meant to write

d/75 + d/r = (dr + 75 d)/(75 r)
=================================

d/75 + d/r = 2d/100

1/r = 2/100 - 1/75 = 6/300 - 4/300 = 1/150

r = 150

To determine how fast Benjamin must go on his second lap to qualify for the race, we need to calculate the average speed he needs for the whole race.

Let's break down the problem and find a solution step by step:

Step 1: Calculate the total distance of the race
Since Benjamin needs to complete 2 laps of the track to qualify for the race, we need to find the total distance of 2 laps.

Step 2: Calculate the time it takes for Benjamin to complete the first lap
To find the time taken for the first lap, we can use the formula: Time = Distance / Speed.
Since we know the average speed for the first lap is 75 mi/h, we can calculate the time taken for the first lap.

Step 3: Calculate the remaining distance
To find the remaining distance for Benjamin's second lap, we need to subtract the distance of the first lap from the total distance.

Step 4: Calculate the average speed needed for the whole race
Now we can calculate the average speed Benjamin needs to achieve for the entire race. To do this, we divide the remaining distance by the remaining time. The remaining distance is the total distance minus the distance of the first lap, and the remaining time is the total time minus the time taken for the first lap.

Step 5: Determine the speed Benjamin needs to go on his second lap
To find out the speed Benjamin needs to go on his second lap, we know that the average speed for the whole race should be 100 mi/h. Since he already completed the first lap at an average speed of 75 mi/h, we can subtract this speed from the required average speed to find the additional speed needed for the second lap.

By following these steps, we can calculate the required speed for Benjamin to qualify for the race.