manishbhusal wrote:

Two friends, Tanaya and Stephen were standing together. Tanaya begins to walk in a straight line away from Stephen at a constant rate of 3 miles per hour. One hour later, Stephen begins to run in a straight line in the exact opposite direction at a constant rate of 9 miles per hour. If both Tanaya and Stephen continue to travel, what is the positive difference between the amount of time it takes Stephen to cover the exact distance that Tanaya has covered and the amount of time it takes Stephen to cover twice the distance that Tanaya has covered?

(A) 60 mins

(B) 72 mins

(C) 90 mins

(D) 100 mins

(E) 120 mins

oh nice..that's a good brain killer.

after 1 hour, tanya traveled for 3 miles. Stephen 0.

after 2 hours, tanya - 6 miles, stephen -9 miles

after 3 hours, tanya 9 miles, stephen - 18 miles.

ok, so stephen needs 2 hours to cover twice the distance tanya has walked.

now, time needed for stephan to cover the same distance tanya has walked.

1 hour -> tanya 3, stephen -0.

we know the rates of each.

in 20 minutes, tanya walks 1 miles, stephen 3.

so after 1h 20 mins, tanya walked 4 miles. stephen in 20 mins - 3 miles.

so if 20 mins for tanya 1 mile and for stephen 3, then in 10 mins, tanya will walk 0.5 miles and stephen 1.5

so...after another 10 mins, tanya 4.5 miles, stephen 4.5 miles.

we can see that stephen needs 30 mins to cover the same distance that tanya has covered.

now, 30-120=-90. since we are asked for the POSITIVE difference, -90*-1 = 90 mins.