A church and a flower shop, 3500 m apart, are situated between Emily's house and Sarah's house. The flower shop is halfway between the two houses
and the church is closer to Sarah's house. Emily and Sarah left their homes at the same time and arrived at the church at the same time. Emily drove at a speed of 66 km/h while Sarah drove at a speed 20 km/h slower than Emily. Leaving your answer in kilometres,
- how much farther did Emily travel than Sarah?
- how far is Sarah's house from the flower shop?
(a)
Let the distance between Emily's house and Sarah's house be 1 d.
Sarah travelled =
12 d - 3500 m
Emily travelled =
12 d + 3500 m
Distance that Emily travelled more than Sarah
=
12 d + 3500 - (
12 d - 3500)
=
12 d + 3500 -
12 d + 3500
= 7000 m
= 7 km
(b)
Time that Emily took to travel to the church
= 7 ÷ 20
=
720 h
Distance that Emily travelled
=
720 x 66
= 23.1 km
1000 m = 1 km
3500 m = 3.5 km
Distance between Sarah's house and the flower shop
= 23.1 - 3.5
= 19.6 km
Answer(s): (a) 7 km; (b) 19.6 km