A pastry shop and a flower shop, 500 m apart, are situated between Esther'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. Esther and Risa left their homes at the same time and arrived at the pastry shop at the same time. Esther drove at a speed of 62 km/h while Risa drove at a speed 20 km/h slower than Esther. Leaving your answer in kilometres,

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

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

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

(b)
Time that Esther took to travel to the pastry shop
= 1 ÷ 20
= ¹₂₀ h

Distance that Esther travelled
= ¹₂₀ x 62
= 3.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Risa's house and the flower shop
= 3.1 - 0.5
= 2.6 km

Answer(s): (a) 1 km; (b) 2.6 km