A pharmacy and a bank, 500 m apart, are situated between Victoria's house and Olivia's house. The bank is halfway between the two houses and the pharmacy is closer to Olivia's house. Victoria and Olivia left their homes at the same time and arrived at the pharmacy at the same time. Victoria drove at a speed of 68 km/h while Olivia drove at a speed 17 km/h slower than Victoria. Leaving your answer in kilometres,

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

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

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

(b)
Time that Victoria took to travel to the pharmacy
= 1 ÷ 17
= ¹₁₇ h

Distance that Victoria travelled
= ¹₁₇ x 68
= 4 km

1000 m = 1 km
500 m = 0.5 km

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

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