.
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.
