Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B,

[BTGmoderatorDC]

Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A?
(A) 60 mph
(B) 75 mph
(C) 80 mph
(D) 96 mph
(E) 100 mph


OA E

Source: Magoosh

[swerve]

Cars A and B are traveling from Town X to Town Y on the same route at constant speeds. Car A is initially behind Car B, and Car A’s speed is 1.25 times Car B’s speed. Car A passes Car B at 1:30 pm. At 3:15 pm, Car A reaches Town Y, and at that moment, Car B is still 35 miles away from Town Y. What is the speed of Car A?
(A) 60 mph
(B) 75 mph
(C) 80 mph
(D) 96 mph
(E) 100 mph


OA E

Source: Magoosh

rate \(a: 1.25b\)
rate \(b: b\)

\(3:15h - 1:30h = 1:45h = \dfrac{105}{60}\)

During this interval:
\(a\) traveled \(\dfrac{105}{60}(1.25b)\)

\(b\) traveled \(\dfrac{105}{60}(b)\)

Their difference is \(35\)
\(35=\dfrac{105}{60}(1.25b) - \dfrac{105}{60}(b)\)
\(b=80\)
\(1.25b=80, b=100 \quad\Longrightarrow\quad\)E