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

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

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

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

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

Distance that Hilda travelled
= ⁵₁₆ x 64
= 20 km

1000 m = 1 km
2500 m = 2.5 km

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

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