A church and a flower shop, 500 m apart, are situated between Gabby's house and Sabrina's house. The flower shop is halfway between the two houses and the church is closer to Sabrina's house. Gabby and Sabrina left their homes at the same time and arrived at the church at the same time. Gabby drove at a speed of 76 km/h while Sabrina drove at a speed 10 km/h slower than Gabby. Leaving your answer in kilometres,

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

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

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

(b)
Time that Gabby took to travel to the church
= 1 ÷ 10
= ¹₁₀ h

Distance that Gabby travelled
= ¹₁₀ x 76
= 7.6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Sabrina's house and the flower shop
= 7.6 - 0.5
= 7.1 km

Answer(s): (a) 1 km; (b) 7.1 km