# The average speed of a pick-up was 20km/h faster than the average speed of a lorry. The pick-up took 45 minutes less than the lorry to cover a distance of 180 km.

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The average speed of a pick-up was 20km/h faster than the average speed of a lorry. The pick-up took 45 minutes less than the lorry to cover a distance of 180 km.

1. If the speed of the lorry was x km/h:
• Write expressions in terms of x for the time taken by the lorry and the pick-up respectively to cover the distance of 180 km
• Determine the speed of the lorry and that of the pick-up.
2. The distance between towns A and B is 240 km. On a certain day the pick-up started from town A at 8.30 a.m. and the lorry started from town B at the same time. Determine the time that the lorry and the pick-up met.

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1.
• lorry time = 180/x km hrs
Pick up time = 180/x+20 km hrs

• 180/km  − 180/x+20 km = 3/4
x2 + 20x − 4800= 0
(x − 60)(x + 80) = 0
x = 60km/h or −80km/h
∴ x = 60km/h
hence lorry = 60km/h &
pick up = 80km/h
2. distance pick up +distance lorry = 240km
80(t − 8.30am) + 60 (t − 8. 30am) = 240
where t meeting time
140t− 680 − 510 = 240
t ≈ 1013hrs