A pharmacy and a bank, 500 m apart, are situated between Fanny's house and Eva's house. The bank is halfway between the two houses and the pharmacy is closer to Eva's house. Fanny and Eva left their homes at the same time and arrived at the pharmacy at the same time. Fanny drove at a speed of 80 km/h while Eva drove at a speed 10 km/h slower than Fanny. Leaving your answer in kilometres,

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

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

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

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

Distance that Fanny travelled
= ¹₁₀ x 80
= 8 km

1000 m = 1 km
500 m = 0.5 km

Distance between Eva's house and the bank
= 8 - 0.5
= 7.5 km

Answer(s): (a) 1 km; (b) 7.5 km