A pastry shop and a flower shop, 500 m apart, are situated between Usha's house and Joelle's house. The flower shop is halfway between the two houses and the pastry shop is closer to Joelle's house. Usha and Joelle left their homes at the same time and arrived at the pastry shop at the same time. Usha drove at a speed of 67 km/h while Joelle drove at a speed 20 km/h slower than Usha. Leaving your answer in kilometres,

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

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

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

(b)
Time that Usha took to travel to the pastry shop
= 1 ÷ 20
= ¹₂₀ h

Distance that Usha travelled
= ¹₂₀ x 67
= 3.35 km

1000 m = 1 km
500 m = 0.5 km

Distance between Joelle's house and the flower shop
= 3.35 - 0.5
= 2.85 km

Answer(s): (a) 1 km; (b) 2.85 km