A pharmacy and a bank, 500 m apart, are situated between Olivia's house and Julie's house. The bank is halfway between the two houses and the pharmacy is closer to Julie's house. Olivia and Julie left their homes at the same time and arrived at the pharmacy at the same time. Olivia drove at a speed of 79 km/h while Julie drove at a speed 20 km/h slower than Olivia. Leaving your answer in kilometres,

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

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

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

(b)
Time that Olivia took to travel to the pharmacy
= 1 ÷ 20
= ¹₂₀ h

Distance that Olivia travelled
= ¹₂₀ x 79
= 3.95 km

1000 m = 1 km
500 m = 0.5 km

Distance between Julie's house and the bank
= 3.95 - 0.5
= 3.45 km

Answer(s): (a) 1 km; (b) 3.45 km