perplexus.info :: General : Time And Distance Problem

Time And Distance Problem (Posted on 2006-12-24)

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 Subject	Jim	2006-12-26 17:31:57
Algebraic solution	Charlie	2006-12-24 14:01:17
Excel solution	Charlie	2006-12-24 13:42:23

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info