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Time And Distance Problem (Posted on 2006-12-24) Difficulty: 2 of 5
Carl has to travel a certain distance. After he has travelled 40 kilometres, he increases his speed by 2 kilometres per hour. If he had travelled with this increased speed during the whole of his journey, he would have arrived 40 minutes earlier at his destination. On the other hand, if he had continued with his original speed, he would have arrived 20 minutes later.

How far did Carl have to travel?

  Submitted by K Sengupta    
Rating: 4.0000 (1 votes)
Solution: (Hide)
Let x be the number of kilometres Carl had to travel; and suppose his original speed was y kilometers per hour.

Hence, the total time taken to complete the journey
= 40/y + (x-40)/(y+2) = (80+xy)/(y^2 + 2y) hours.

Hence, we obtain:

x/(y+2) = (80+xy)/(y^2 + 2y) - 2/3-----(1)

x/y = (80+xy)/(y^2 + 2y) + 1/3------(2)

Subtracting (1) from (2):

2x = y(y+2).......(3)
Also, from (2)
3x(y+2) = 3(80+xy) + y(y+2)
or, 6x - 240 = y(y+2)
or, 6x - 240 = 2x ( form (3) ); giving, x = 60

Consequently, Carl had to travel 60 Kilometres.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
No SubjectJim2006-12-26 17:31:57
SolutionAlgebraic solutionCharlie2006-12-24 14:01:17
SolutionExcel solutionCharlie2006-12-24 13:42:23
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