A pharmacy and a bank, 2500 m apart, are situated between Eva's house and Fiona's house. The bank is halfway between the two houses and the pharmacy is closer to Fiona's house. Eva and Fiona left their homes at the same time and arrived at the pharmacy at the same time. Eva drove at a speed of 76 km/h while Fiona drove at a speed 19 km/h slower than Eva. Leaving your answer in kilometres,

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

(a)
Let the distance between Eva's house and Fiona's house be 1 d.
Fiona travelled = ¹₂ d - 2500 m
Eva travelled = ¹₂ d + 2500 m

Distance that Eva travelled more than Fiona
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Eva took to travel to the pharmacy
= 5 ÷ 19
= ⁵₁₉ h

Distance that Eva travelled
= ⁵₁₉ x 76
= 20 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Fiona's house and the bank
= 20 - 2.5
= 17.5 km

Answer(s): (a) 5 km; (b) 17.5 km