A pharmacy and a bank, 500 m apart, are situated between Natalie's house and Wendy's house. The bank is halfway between the two houses and the pharmacy is closer to Wendy's house. Natalie and Wendy left their homes at the same time and arrived at the pharmacy at the same time. Natalie drove at a speed of 79 km/h while Wendy drove at a speed 10 km/h slower than Natalie. Leaving your answer in kilometres,

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

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

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

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

Distance that Natalie travelled
= ¹₁₀ x 79
= 7.9 km

1000 m = 1 km
500 m = 0.5 km

Distance between Wendy's house and the bank
= 7.9 - 0.5
= 7.4 km

Answer(s): (a) 1 km; (b) 7.4 km