A pharmacy and a bank, 2500 m apart, are situated between Fiona's house and Elyse's house. The bank is halfway between the two houses and the pharmacy is closer to Elyse's house. Fiona and Elyse left their homes at the same time and arrived at the pharmacy at the same time. Fiona drove at a speed of 72 km/h while Elyse drove at a speed 16 km/h slower than Fiona. Leaving your answer in kilometres,

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

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

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

(b)
Time that Fiona took to travel to the pharmacy
= 5 ÷ 16
= ⁵₁₆ h

Distance that Fiona travelled
= ⁵₁₆ x 72
= 22.5 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Elyse's house and the bank
= 22.5 - 2.5
= 20 km

Answer(s): (a) 5 km; (b) 20 km