A pharmacy and a bank, 500 m apart, are situated between Kimberly's house and Victoria's house. The bank is halfway between the two houses and the pharmacy is closer to Victoria's house. Kimberly and Victoria left their homes at the same time and arrived at the pharmacy at the same time. Kimberly drove at a speed of 64 km/h while Victoria drove at a speed 10 km/h slower than Kimberly. Leaving your answer in kilometres,

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

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

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

(b)
Time that Kimberly took to travel to the pharmacy
= 1 ÷ 10
= ¹₁₀ h

Distance that Kimberly travelled
= ¹₁₀ x 64
= 6.4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Victoria's house and the bank
= 6.4 - 0.5
= 5.9 km

Answer(s): (a) 1 km; (b) 5.9 km