A church and a flower shop, 500 m apart, are situated between Shiyun's house and Barbara's house. The flower shop is halfway between the two houses and the church is closer to Barbara's house. Shiyun and Barbara left their homes at the same time and arrived at the church at the same time. Shiyun drove at a speed of 61 km/h while Barbara drove at a speed 20 km/h slower than Shiyun. Leaving your answer in kilometres,

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

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

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

(b)
Time that Shiyun took to travel to the church
= 1 ÷ 20
= ¹₂₀ h

Distance that Shiyun travelled
= ¹₂₀ x 61
= 3.05 km

1000 m = 1 km
500 m = 0.5 km

Distance between Barbara's house and the flower shop
= 3.05 - 0.5
= 2.55 km

Answer(s): (a) 1 km; (b) 2.55 km