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

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

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

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

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

Distance that Emma travelled
= ³₂₀ x 65
= 9.75 km

1000 m = 1 km
1500 m = 1.5 km

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

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