SOLUTION: Hi Town A and B are 220km apart. A lorry driver and a taxi driver started off at the same time from town A. The taxi driver reached B 1 and 2/3 hours ahead of the lorry driver wh

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Question 1118668: Hi
Town A and B are 220km apart. A lorry driver and a taxi driver started off at the same time from town A. The taxi driver reached B 1 and 2/3 hours ahead of the lorry driver who still had 100km to go.
what was the speed of the lorry driver
what was the speed of the taxi driver.
Thanks
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
Answer by greenestamps(13209) About Me  (Show Source):
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Tutor @josgarithmetic misinterpreted the given information and so solved the wrong problem. The 1 2/3 hours is the DIFFERENCE between the times it took the taxi and the lorry to make the whole trip; it is not the amount of time the taxi took to make the trip.

Let x be the speed of the taxi and y the speed of the lorry. Then

The difference between the time required by the lorry to make the full trip and the time required by the taxi was 1 2/3 hours, or 5/3 hours:
(1) 220%2Fy+=+220%2Fx%2B5%2F3

The time required for the taxi to go the full 220km is equal to the time required for the lorry to go 220-100 = 120km:
(2) 220%2Fx+=+120%2Fy

Substitute (2) into (1):

220%2Fy+=+120%2Fy%2B5%2F3
100%2Fy+=+5%2F3
y+=+100%283%2F5%29+=+60

The speed of the lorry was 60km/hr.

Substitute y=60 into (2):
(3) 220%2Fx+=+120%2F60
220%2Fx+=+2
x+=+110

The speed of the taxi was 110km/hr.