A salon and a cafe, 500 m apart, are situated between Tammy's house and Dana's house. The cafe is halfway between the two houses and the salon is closer to Dana's house. Tammy and Dana left their homes at the same time and arrived at the salon at the same time. Tammy drove at a speed of 61 km/h while Dana drove at a speed 10 km/h slower than Tammy. Leaving your answer in kilometres,

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

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

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

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

Distance that Tammy travelled
= ¹₁₀ x 61
= 6.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Dana's house and the cafe
= 6.1 - 0.5
= 5.6 km

Answer(s): (a) 1 km; (b) 5.6 km