A salon and a cafe, 3500 m apart, are situated between Xuan's house and Tammy's house. The cafe is halfway between the two houses and the salon is closer to Tammy's house. Xuan and Tammy left their homes at the same time and arrived at the salon at the same time. Xuan drove at a speed of 62 km/h while Tammy drove at a speed 20 km/h slower than Xuan. Leaving your answer in kilometres,

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

(a)
Let the distance between Xuan's house and Tammy's house be 1 d.
Tammy travelled = ¹₂ d - 3500 m
Xuan travelled = ¹₂ d + 3500 m

Distance that Xuan travelled more than Tammy
= ¹₂ d + 3500 - (¹₂ d - 3500)
= ¹₂ d + 3500 - ¹₂ d + 3500
= 7000 m
= 7 km

(b)
Time that Xuan took to travel to the salon
= 7 ÷ 20
= ⁷₂₀ h

Distance that Xuan travelled
= ⁷₂₀ x 62
= 21.7 km

1000 m = 1 km
3500 m = 3.5 km

Distance between Tammy's house and the cafe
= 21.7 - 3.5
= 18.2 km

Answer(s): (a) 7 km; (b) 18.2 km