A pharmacy and a bank, 500 m apart, are situated between Joelle's house and Cathy's house. The bank is halfway between the two houses and the pharmacy is closer to Cathy's house. Joelle and Cathy left their homes at the same time and arrived at the pharmacy at the same time. Joelle drove at a speed of 66 km/h while Cathy drove at a speed 12 km/h slower than Joelle. Leaving your answer in kilometres,

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

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

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

(b)
Time that Joelle took to travel to the pharmacy
= 1 ÷ 12
= ¹₁₂ h

Distance that Joelle travelled
= ¹₁₂ x 66
= 5.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Cathy's house and the bank
= 5.5 - 0.5
= 5 km

Answer(s): (a) 1 km; (b) 5 km