A salon and a cafe, 500 m apart, are situated between Jean's house and Tammy's house. The cafe is halfway between the two houses and the salon is closer to Tammy's house. Jean and Tammy left their homes at the same time and arrived at the salon at the same time. Jean drove at a speed of 75 km/h while Tammy drove at a speed 10 km/h slower than Jean. Leaving your answer in kilometres,

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

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

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

(b)
Time that Jean took to travel to the salon
= 1 ÷ 10
= ¹₁₀ h

Distance that Jean travelled
= ¹₁₀ x 75
= 7.5 km

1000 m = 1 km
500 m = 0.5 km

Distance between Tammy's house and the cafe
= 7.5 - 0.5
= 7 km

Answer(s): (a) 1 km; (b) 7 km