inequalities

Peter drive his car for 18 minutes and Mary drives her car for 15 minutes. It is known that both of them drive at uniform speeds and the total distance travelled by Peter exceeds that of Mary by 2 km. If at least one of their cars does not exceed 80 km/h, find the maximum possible distance that Peter travels.

Let p km/h be the speed of Peter, and m km/h be that of Mary.

p x (18/60) - m x (15/60) = 2
0.3p - 0.25m = 2
0.25m = 0.3p - 2
m = (0.3p - 2)/0.25

p ≤ 80 or m ≤ 80
p ≤ 80 or (0.3p - 2)/0.25 ≤ 80
p ≤ 80 or (0.3p - 2) ≤ 20
p ≤ 80 or 0.3p ≤ 22
p ≤ 80 or p ≤ 73.33

Hence, the maximum possible speed of Peter
= 80 km/h

Maximum possible distance that Peter travels
= 80 x (18/60)
= 24 km