Tina and Sarah decided to meet at a park bench near both of

Tina and Sarah decided to meet at a park bench near both of their homes. Tina lives 2050 feet due west of the park bench and Sarah lives 1650 feet due east of the park bench. Sarah left her house at 7:00 pm and traveled at a constant speed of 300 feet per minute towards the bench. Tina left her house at the same time traveling a constant speed of 350 feet per minute towards the bench.

A. Define a formula that relates the distance between Tina and Sarah in terms of the number of minutes since 7:00pm.

B. How far are Tina and Sarah apart 4 minutes after 7:00 pm?

Solution

Distance between the two = 2050 +1650 feet (opposite direction)

After t minutes they left:

distance travlled by Tina = speed*time = 300*t

distance travlled by Sarah = speed*time = 350*t

A) So, distance between the two = 3700 - 300t -350t = 3700 - 650t

B) After t = 4minutes

distance between the two = 3700 - 650*4 = 1100 feet