SOLUTION: Hi A delivery van was travelling at an average speed of 50km per hour for the first 20 minutes. The driver took a wrong turn and realised that he would be late by 10 minutes. He t

Question 1208623: Hi
A delivery van was travelling at an average speed of 50km per hour for the first 20 minutes. The driver took a wrong turn and realised that he would be late by 10 minutes. He then increased his speed to 75km per hour. When he arrived he was early by 6 minutes. How far did he travel.
Answer by ikleyn(52750) (Show Source): You can put this solution on YOUR website!
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A delivery van was travelling at an average speed of 50 km per hour for the first 20 minutes.
The driver took a wrong turn and realized that he would be late by 10 minutes.
He then increased his speed to 75 km per hour. When he arrived he was early by 6 minutes. How far did he travel.
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The entire trip consists of two parts.

First part length is the product of the speed 50 km/h by the time of 20 minutes, which is 1/3 of an hour.

So, the first part length is   = 16 kilometers.


Let "d" be the length of the second part of the trip.


About the second part of the trip, we know that if the driver travels at 50 km/h, he would be late by 10 minutes;
                                                                                   
                                                if the driver travels at 75 km/h, he would be earlier by 6 minutes.


It gives us this time equation for the difference of travel times

     -  =  + ,

or

     -  = .


Simplify it step by step and find "d"

     = ,

     = ,

     = ,

    d =  =  = 40.


Thus the second part length is 40 kilometers.


Now the ANSWER to the problem's question is the sum   16 + 40 = 56 kilometers.

Solved.

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