A pastry shop and a flower shop, 2500 m apart, are situated between Victoria's house and Emily's house. The flower shop is halfway between the two houses and the pastry shop is closer to Emily's house. Victoria and Emily left their homes at the same time and arrived at the pastry shop at the same time. Victoria drove at a speed of 64 km/h while Emily drove at a speed 16 km/h slower than Victoria. Leaving your answer in kilometres,

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

(a)
Let the distance between Victoria's house and Emily's house be 1 d.
Emily travelled = ¹₂ d - 2500 m
Victoria travelled = ¹₂ d + 2500 m

Distance that Victoria travelled more than Emily
= ¹₂ d + 2500 - (¹₂ d - 2500)
= ¹₂ d + 2500 - ¹₂ d + 2500
= 5000 m
= 5 km

(b)
Time that Victoria took to travel to the pastry shop
= 5 ÷ 16
= ⁵₁₆ h

Distance that Victoria travelled
= ⁵₁₆ x 64
= 20 km

1000 m = 1 km
2500 m = 2.5 km

Distance between Emily's house and the flower shop
= 20 - 2.5
= 17.5 km

Answer(s): (a) 5 km; (b) 17.5 km