A pharmacy and a bank, 500 m apart, are situated between Cathy's house and Jean's house. The bank is halfway between the two houses and the pharmacy is closer to Jean's house. Cathy and Jean left their homes at the same time and arrived at the pharmacy at the same time. Cathy drove at a speed of 60 km/h while Jean drove at a speed 15 km/h slower than Cathy. Leaving your answer in kilometres,

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

(a)
Let the distance between Cathy's house and Jean's house be 1 d.
Jean travelled = ¹₂ d - 500 m
Cathy travelled = ¹₂ d + 500 m

Distance that Cathy travelled more than Jean
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Cathy took to travel to the pharmacy
= 1 ÷ 15
= ¹₁₅ h

Distance that Cathy travelled
= ¹₁₅ x 60
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Jean's house and the bank
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km