A pharmacy and a bank, 500 m apart, are situated between Xuan's house and Esther's house. The bank is halfway between the two houses and the pharmacy is closer to Esther's house. Xuan and Esther left their homes at the same time and arrived at the pharmacy at the same time. Xuan drove at a speed of 75 km/h while Esther drove at a speed 10 km/h slower than Xuan. Leaving your answer in kilometres,

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

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

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

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

Distance that Xuan travelled
= ¹₁₀ x 75
= 7.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Esther's house and the bank
= 7.5 - 0.5
= 7 km

Answer(s): (a) 1 km; (b) 7 km