A pastry shop and a flower shop, 500 m apart, are situated between Penelope's house and Wendy's house. The flower shop is halfway between the two houses and the pastry shop is closer to Wendy's house. Penelope and Wendy left their homes at the same time and arrived at the pastry shop at the same time. Penelope drove at a speed of 60 km/h while Wendy drove at a speed 15 km/h slower than Penelope. Leaving your answer in kilometres,

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

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

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

(b)
Time that Penelope took to travel to the pastry shop
= 1 ÷ 15
= ¹₁₅ h

Distance that Penelope travelled
= ¹₁₅ x 60
= 4 km

1000 m = 1 km
500 m = 0.5 km

Distance between Wendy's house and the flower shop
= 4 - 0.5
= 3.5 km

Answer(s): (a) 1 km; (b) 3.5 km