At 8 a.m., Archie started from City S and travelled towards City T and his speed remained constant throughout. At 10 a.m., Gabby started her journey from City S towards City T at an average speed of 90 km/h. Gabby overtook Archie at 1 p.m. After overtaking, Gabby carried on her journey at the same average speed and reached at City T at 5:50 p.m.

1. Find Archie'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 Gabby had travelled until Gabby overtook Archie
= 3 x 90
= 270 km

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

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

(b)
From 10 a.m. to 5:50 p.m. = 7 h 50 min

1 h = 60 min
7 h 50 min = 7 ⁵⁰ ₆₀
 h = 7 ⁵₆ h

Distance between the two cities
= 7 ⁵₆ x 90
= ⁴⁷₆ x 90
= 705 km

Answer(s): (a) 54 km/h; (b) 705 km