A pastry shop and a flower shop, 1000 m apart, are situated between Roshel'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. Roshel and Jen left their homes at the same time and arrived at the pastry shop at the same time. Roshel drove at a speed of 60 km/h while Jen drove at a speed 15 km/h slower than Roshel. Leaving your answer in kilometres,

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

(a)
Let the distance between Roshel's house and Jen's house be 1 d.
Jen travelled = ¹₂ d - 1000 m
Roshel travelled = ¹₂ d + 1000 m

Distance that Roshel travelled more than Jen
= ¹₂ d + 1000 - (¹₂ d - 1000)
= ¹₂ d + 1000 - ¹₂ d + 1000
= 2000 m
= 2 km

(b)
Time that Roshel took to travel to the pastry shop
= 2 ÷ 15
= ²₁₅ h

Distance that Roshel travelled
= ²₁₅ x 60
= 8 km

1000 m = 1 km
1000 m = 1 km

Distance between Jen's house and the flower shop
= 8 - 1
= 7 km

Answer(s): (a) 2 km; (b) 7 km