A pharmacy and a bank, 1500 m apart, are situated between Penelope's house and Hilda's house. The bank is halfway between the two houses and the pharmacy is closer to Hilda's house. Penelope and Hilda left their homes at the same time and arrived at the pharmacy at the same time. Penelope drove at a speed of 65 km/h while Hilda drove at a speed 20 km/h slower than Penelope. Leaving your answer in kilometres,

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

(a)
Let the distance between Penelope's house and Hilda's house be 1 d.
Hilda travelled = ¹₂ d - 1500 m
Penelope travelled = ¹₂ d + 1500 m

Distance that Penelope travelled more than Hilda
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Penelope took to travel to the pharmacy
= 3 ÷ 20
= ³₂₀ h

Distance that Penelope travelled
= ³₂₀ x 65
= 9.75 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Hilda's house and the bank
= 9.75 - 1.5
= 8.25 km

Answer(s): (a) 3 km; (b) 8.25 km