Problem Solving

Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?


A)4pie - 1.6

B)4pie + 8.4

C)4pie + 10.4

D)2pie - 1.6

E)2pie - 0.8



OAB

Car B starts at point X and moves clockwise around a circular track at a constant rate of 2 mph. Ten hours later, Car A leaves from point X and travels counter-clockwise around the same circular track at a constant rate of 3 mph. If the radius of the track is 10 miles, for how many hours will Car B have been traveling when the cars have passed each other for the first time and put another 12 miles between them (measured around the curve of the track)?
a) 4pi- 1.6
b) 4pi+ 8.4
c) 4pi+ 10.4
d) 2pi- 1.6
e) 2pi- 0.8

π ≈ 3.

Car B is traveling for more than 10 hours, so answer choices D and E are too small, and A is unlikely. The correct answer is either B or C.

Circumference of track = 20π ≈ 60 miles.
In 10 hours, distance for B = 2*10 = 20 miles.
60-20 = 40 miles between A and B.
A and B now have to travel the 40 miles between them and then -- after they meet -- keep traveling in opposite directions until there is another 12 miles between them. So the total distance that they need to travel is 40+12 = 52 miles.
When things work together, we can add their rates. Combined rate for A+B = 3+2 = 5 miles/hour.
Time for A+B = Distance/Rate = 52/5 = 10.4 hours.
Since B traveled for 10 hours before A joined in, the total time for B = 10 + 10.4 = 20.4 hours.
Only answer choice B works: 4π + 8.4 ≈ 12 + 8.4 = 20.4.

The correct answer is B

radius of track = 10 m
circumpherence = 20pie


B at speed of 2mph runs for 10 hrs = 20miles

now A started from opposite side at 3 mph

now relative speed = 2 + 3 = 5

consider A as stand still & B coming at 5 mph from opposite direction

total distance for B to meet A & run 12 mils pass it == 20 pie - 20 + 12

= 20 pie -8

time taken = (20 pie -8)/5 = 4pie -1.6

now B has already ran for 10 hours so total time taken by B is 10 + 4 pie -1.6 = 4 pie + 8.4

Answer B