A pharmacy and a bank, 1500 m apart, are situated between Xuan's house and Linda's house. The bank is halfway between the two houses and the pharmacy is closer to Linda's house. Xuan and Linda left their homes at the same time and arrived at the pharmacy at the same time. Xuan drove at a speed of 74 km/h while Linda drove at a speed 20 km/h slower than Xuan. Leaving your answer in kilometres,

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

(a)
Let the distance between Xuan's house and Linda's house be 1 d.
Linda travelled = ¹₂ d - 1500 m
Xuan travelled = ¹₂ d + 1500 m

Distance that Xuan travelled more than Linda
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Xuan took to travel to the pharmacy
= 3 ÷ 20
= ³₂₀ h

Distance that Xuan travelled
= ³₂₀ x 74
= 11.1 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Linda's house and the bank
= 11.1 - 1.5
= 9.6 km

Answer(s): (a) 3 km; (b) 9.6 km