A pastry shop and a flower shop, 1500 m apart, are situated between Usha's house and Hilda's house. The flower shop is halfway between the two houses and the pastry shop is closer to Hilda's house. Usha and Hilda left their homes at the same time and arrived at the pastry shop at the same time. Usha drove at a speed of 64 km/h while Hilda drove at a speed 16 km/h slower than Usha. Leaving your answer in kilometres,

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

(a)
Let the distance between Usha's house and Hilda's house be 1 d.
Hilda travelled = ¹₂ d - 1500 m
Usha travelled = ¹₂ d + 1500 m

Distance that Usha travelled more than Hilda
= ¹₂ d + 1500 - (¹₂ d - 1500)
= ¹₂ d + 1500 - ¹₂ d + 1500
= 3000 m
= 3 km

(b)
Time that Usha took to travel to the pastry shop
= 3 ÷ 16
= ³₁₆ h

Distance that Usha travelled
= ³₁₆ x 64
= 12 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Hilda's house and the flower shop
= 12 - 1.5
= 10.5 km

Answer(s): (a) 3 km; (b) 10.5 km