A pharmacy and a bank, 1500 m apart, are situated between Joelle's house and Kylie's house. The bank is halfway between the two houses and the pharmacy is closer to Kylie's house. Joelle and Kylie left their homes at the same time and arrived at the pharmacy at the same time. Joelle drove at a speed of 77 km/h while Kylie drove at a speed 20 km/h slower than Joelle. Leaving your answer in kilometres,

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

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

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

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

Distance that Joelle travelled
= ³₂₀ x 77
= 11.55 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Kylie's house and the bank
= 11.55 - 1.5
= 10.05 km

Answer(s): (a) 3 km; (b) 10.05 km