A pastry shop and a flower shop, 500 m apart, are situated between Jane's house and Hazel's house. The flower shop is halfway between the two houses and the pastry shop is closer to Hazel's house. Jane and Hazel left their homes at the same time and arrived at the pastry shop at the same time. Jane drove at a speed of 72 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 flower shop?

(a)
Let the distance between Jane's house and Hazel's house be 1 d.
Hazel travelled = ¹₂ d - 500 m
Jane travelled = ¹₂ d + 500 m

Distance that Jane travelled more than Hazel
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Jane took to travel to the pastry shop
= 1 ÷ 16
= ¹₁₆ h

Distance that Jane travelled
= ¹₁₆ x 72
= 4.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Hazel's house and the flower shop
= 4.5 - 0.5
= 4 km

Answer(s): (a) 1 km; (b) 4 km