At 9 a.m., Tom started from City Q and travelled towards City R and his speed remained constant throughout. At 10 a.m., Lucy started her journey from City Q towards City R at an average speed of 72 km/h. Lucy overtook Tom at 3 p.m. After overtaking, Lucy carried on her journey at the same average speed and reached at City R at 5:25 p.m.

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

(a)
From 10 a.m. to 3 p.m. = 5 h

Distance that Lucy had travelled until Lucy overtook Tom
= 5 x 72
= 360 km

From 9 a.m. to 3 p.m. = 6 h

Tom's average speed
= 360 ÷ 6
= 60 km/h

(b)
From 10 a.m. to 5:25 p.m. = 7 h 25 min

1 h = 60 min
7 h 25 min = 7 ²⁵ ₆₀
 h = 7 ⁵₁₂ h

Distance between the two cities
= 7 ⁵₁₂ x 72
= ⁸⁹₁₂ x 72
= 534 km

Answer(s): (a) 60 km/h; (b) 534 km