At 8 a.m., Carl started from City T and travelled towards City U and his speed remained constant throughout. At 10 a.m., Emily started her journey from City T towards City U at an average speed of 90 km/h. Emily overtook Carl at 1 p.m. After overtaking, Emily carried on her journey at the same average speed and reached at City U at 6:30 p.m.

1. Find Carl's average speed in km/h.
2. What is the distance between the two cities?

(a)
From 10 a.m. to 1 p.m. = 3 h

Distance that Emily had travelled until Emily overtook Carl
= 3 x 90
= 270 km

From 8 a.m. to 1 p.m. = 5 h

Carl's average speed
= 270 ÷ 5
= 54 km/h

(b)
From 10 a.m. to 6:30 p.m. = 8 h 30 min

1 h = 60 min
8 h 30 min = 8 ³⁰ ₆₀
 h = 8 ¹₂ h

Distance between the two cities
= 8 ¹₂ x 90
= ¹⁷₂ x 90
= 765 km

Answer(s): (a) 54 km/h; (b) 765 km