A pharmacy and a bank, 3500 m apart, are situated between Penelope's house and Abi's house. The bank is halfway between the two houses and the pharmacy is closer to Abi's house. Penelope and Abi left their homes at the same time and arrived at the pharmacy at the same time. Penelope drove at a speed of 60 km/h while Abi drove at a speed 20 km/h slower than Penelope. Leaving your answer in kilometres,

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

(a)
Let the distance between Penelope's house and Abi's house be 1 d.
Abi travelled = ¹₂ d - 3500 m
Penelope travelled = ¹₂ d + 3500 m

Distance that Penelope travelled more than Abi
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Penelope took to travel to the pharmacy
= 7 ÷ 20
= ⁷₂₀ h

Distance that Penelope travelled
= ⁷₂₀ x 60
= 21 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Abi's house and the bank
= 21 - 3.5
= 17.5 km

Answer(s): (a) 7 km; (b) 17.5 km