A pharmacy and a bank, 500 m apart, are situated between Emily's house and Hilda's house. The bank is halfway between the two houses and the pharmacy is closer to Hilda's house. Emily and Hilda left their homes at the same time and arrived at the pharmacy at the same time. Emily drove at a speed of 71 km/h while Hilda drove at a speed 10 km/h slower than Emily. Leaving your answer in kilometres,

1. how much farther did Emily travel than Hilda?
2. how far is Hilda's house from the bank?

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

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

(b)
Time that Emily took to travel to the pharmacy
= 1 ÷ 10
= ¹₁₀ h

Distance that Emily travelled
= ¹₁₀ x 71
= 7.1 km

1000 m = 1 km
500 m = 0.5 km

Distance between Hilda's house and the bank
= 7.1 - 0.5
= 6.6 km

Answer(s): (a) 1 km; (b) 6.6 km