A church and a flower shop, 500 m apart, are situated between Usha's house and Elyse's house. The flower shop is halfway between the two houses and the church is closer to Elyse's house. Usha and Elyse left their homes at the same time and arrived at the church at the same time. Usha drove at a speed of 62 km/h while Elyse drove at a speed 10 km/h slower than Usha. Leaving your answer in kilometres,

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

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

Distance that Usha travelled more than Elyse
= 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 church
= 1 ÷ 10
= ¹₁₀ h

Distance that Usha travelled
= ¹₁₀ x 62
= 6.2 km

1000 m = 1 km
500 m = 0.5 km

Distance between Elyse's house and the flower shop
= 6.2 - 0.5
= 5.7 km

Answer(s): (a) 1 km; (b) 5.7 km