A salon and a cafe, 500 m apart, are situated between Usha's house and Mary's house. The cafe is halfway between the two houses and the salon is closer to Mary's house. Usha and Mary left their homes at the same time and arrived at the salon at the same time. Usha drove at a speed of 67 km/h while Mary drove at a speed 10 km/h slower than Usha. Leaving your answer in kilometres,

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

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

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

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

Distance that Usha travelled
= ¹₁₀ x 67
= 6.7 km

1000 m = 1 km
500 m = 0.5 km

Distance between Mary's house and the cafe
= 6.7 - 0.5
= 6.2 km

Answer(s): (a) 1 km; (b) 6.2 km