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

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

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

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

(b)
Time that Opal took to travel to the pastry shop
= 3 ÷ 16
= ³₁₆ h

Distance that Opal travelled
= ³₁₆ x 64
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Ivory's house and the flower shop
= 12 - 1.5
= 10.5 km

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