math
posted by monica on .
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