A pastry shop and a flower shop, 3500 m apart, are situated between Dana's house and Jen's house. The flower shop is halfway between the two houses and the pastry shop is closer to Jen's house. Dana and Jen left their homes at the same time and arrived at the pastry shop at the same time. Dana drove at a speed of 64 km/h while Jen drove at a speed 20 km/h slower than Dana. Leaving your answer in kilometres,

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

(a)
Let the distance between Dana's house and Jen's house be 1 d.
Jen travelled = ¹₂ d - 3500 m
Dana travelled = ¹₂ d + 3500 m

Distance that Dana travelled more than Jen
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Dana took to travel to the pastry shop
= 7 ÷ 20
= ⁷₂₀ h

Distance that Dana travelled
= ⁷₂₀ x 64
= 22.4 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Jen's house and the flower shop
= 22.4 - 3.5
= 18.9 km

Answer(s): (a) 7 km; (b) 18.9 km