A salon and a cafe, 1500 m apart, are situated between Linda's house and Mary's house. The cafe is halfway between the two houses and the salon is closer to Mary's house. Linda and Mary left their homes at the same time and arrived at the salon at the same time. Linda drove at a speed of 63 km/h while Mary drove at a speed 20 km/h slower than Linda. Leaving your answer in kilometres,

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

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

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

(b)
Time that Linda took to travel to the salon
= 3 ÷ 20
= ³₂₀ h

Distance that Linda travelled
= ³₂₀ x 63
= 9.45 km

1000 m = 1 km
1500 m = 1.5 km

Distance between Mary's house and the cafe
= 9.45 - 1.5
= 7.95 km

Answer(s): (a) 3 km; (b) 7.95 km