A pastry shop and a flower shop, 500 m apart, are situated between Jane's house and Risa's house. The flower shop is halfway between the two houses and the pastry shop is closer to Risa's house. Jane and Risa left their homes at the same time and arrived at the pastry shop at the same time. Jane drove at a speed of 69 km/h while Risa drove at a speed 15 km/h slower than Jane. Leaving your answer in kilometres,

1. how much farther did Jane travel than Risa?
2. how far is Risa's house from the flower shop?

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

Distance that Jane travelled more than Risa
= 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 ÷ 15
= ¹₁₅ h

Distance that Jane travelled
= ¹₁₅ x 69
= 4.6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Risa's house and the flower shop
= 4.6 - 0.5
= 4.1 km

Answer(s): (a) 1 km; (b) 4.1 km