A pastry shop and a flower shop, 1500 m apart, are situated between Fiona's house and Yen's house. The flower shop is halfway between the two houses and the pastry shop is closer to Yen's house. Fiona and Yen left their homes at the same time and arrived at the pastry shop at the same time. Fiona drove at a speed of 63 km/h while Yen drove at a speed 14 km/h slower than Fiona. Leaving your answer in kilometres,

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

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

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

(b)
Time that Fiona took to travel to the pastry shop
= 3 ÷ 14
= ³₁₄ h

Distance that Fiona travelled
= ³₁₄ x 63
= 13.5 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Yen's house and the flower shop
= 13.5 - 1.5
= 12 km

Answer(s): (a) 3 km; (b) 12 km