A salon and a cafe, 500 m apart, are situated between Jade's house and Betty's house. The cafe is halfway between the two houses and the salon is closer to Betty's house. Jade and Betty left their homes at the same time and arrived at the salon at the same time. Jade drove at a speed of 72 km/h while Betty drove at a speed 12 km/h slower than Jade. Leaving your answer in kilometres,

1. how much farther did Jade travel than Betty?
2. how far is Betty's house from the cafe?

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

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

(b)
Time that Jade took to travel to the salon
= 1 ÷ 12
= ¹₁₂ h

Distance that Jade travelled
= ¹₁₂ x 72
= 6 km

1000 m = 1 km
500 m = 0.5 km

Distance between Betty's house and the cafe
= 6 - 0.5
= 5.5 km

Answer(s): (a) 1 km; (b) 5.5 km