A pharmacy and a bank, 2000 m apart, are situated between Nicole's house and Penelope's house. The bank is halfway between the two houses and the pharmacy is closer to Penelope's house. Nicole and Penelope left their homes at the same time and arrived at the pharmacy at the same time. Nicole drove at a speed of 65 km/h while Penelope drove at a speed 13 km/h slower than Nicole. Leaving your answer in kilometres,

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

(a)
Let the distance between Nicole's house and Penelope's house be 1 d.
Penelope travelled = ¹₂ d - 2000 m
Nicole travelled = ¹₂ d + 2000 m

Distance that Nicole travelled more than Penelope
= ¹₂ d + 2000 - (¹₂ d - 2000)
= ¹₂ d + 2000 - ¹₂ d + 2000
= 4000 m
= 4 km

(b)
Time that Nicole took to travel to the pharmacy
= 4 ÷ 13
= ⁴₁₃ h

Distance that Nicole travelled
= ⁴₁₃ x 65
= 20 km

1000 m = 1 km
2000 m = 2 km

Distance between Penelope's house and the bank
= 20 - 2
= 18 km

Answer(s): (a) 4 km; (b) 18 km