Answer:
speed of slower driver 30 mph
speed of faster driver = 55 mph
Step-by-step explanation:
let the speed of slower driver b x mph
given
One driver drives 25 mph faster than another driver does
Speed of faster driver = (x+25) mph
we know time = speed / distance
also in same time faster will travel more distance than the slower one.
thus
driver with speed (x+25) mph would have traveled 165 miles
driver with speed x mph would have traveled 90 miles
time for driver with speed (x+25) mph = 165/(x+25)
time for driver with speed x mph = 90/x
Given that
They start at the same time and after a certain amount of time, one driver has driven 90 miles, and the other driver has driven 165 miles.
\time for driver with speed (x+25) mph =time for driver with speed x mph
165/(x+25) = 90/x
165x = 90(x+25)
=> 165x = 90x + 2250
=> 165x -90x = 2250
=> 75x = 2250
=> x = 2250/75= 30
Thus, speed of slower driver 30 mph
speed of faster driver = 30+25 = 55 mph
