A pharmacy and a bank, 1500 m apart, are situated between Jane's house and Hazel's house. The bank is halfway between the two houses and the pharmacy is closer to Hazel's house. Jane and Hazel left their homes at the same time and arrived at the pharmacy at the same time. Jane drove at a speed of 64 km/h while Hazel drove at a speed 16 km/h slower than Jane. Leaving your answer in kilometres,

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

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

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

(b)
Time that Jane took to travel to the pharmacy
= 3 ÷ 16
= ³₁₆ h

Distance that Jane travelled
= ³₁₆ x 64
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Hazel's house and the bank
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km