A pharmacy and a bank, 2500 m apart, are situated between Kathy's house and Sabrina's house. The bank is halfway between the two houses and the pharmacy is closer to Sabrina's house. Kathy and Sabrina left their homes at the same time and arrived at the pharmacy at the same time. Kathy drove at a speed of 63 km/h while Sabrina drove at a speed 14 km/h slower than Kathy. Leaving your answer in kilometres,

1. how much farther did Kathy travel than Sabrina?
2. how far is Sabrina's house from the bank?

(a)
Let the distance between Kathy's house and Sabrina's house be 1 d.
Sabrina travelled = ¹₂ d - 2500 m
Kathy travelled = ¹₂ d + 2500 m

Distance that Kathy travelled more than Sabrina
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Kathy took to travel to the pharmacy
= 5 ÷ 14
= ⁵₁₄ h

Distance that Kathy travelled
= ⁵₁₄ x 63
= 22.5 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Sabrina's house and the bank
= 22.5 - 2.5
= 20 km

Answer(s): (a) 5 km; (b) 20 km