A pharmacy and a bank, 1500 m apart, are situated between Jade's house and Lucy's house. The bank is halfway between the two houses and the pharmacy is closer to Lucy's house. Jade and Lucy left their homes at the same time and arrived at the pharmacy at the same time. Jade drove at a speed of 74 km/h while Lucy drove at a speed 20 km/h slower than Jade. Leaving your answer in kilometres,

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

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

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

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

Distance that Jade travelled
= ³₂₀ x 74
= 11.1 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Lucy's house and the bank
= 11.1 - 1.5
= 9.6 km

Answer(s): (a) 3 km; (b) 9.6 km