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An automobile driver traveled the first part of a 400 mile trip at a average rate of 50 miles per hour.Upon reaching an interstate route his average speed increased to 60 miles per hour his total travel time was 7 hours how far had he traveled when reached the interstate route

Respuesta :

Answer:

The distance travelled is 100 miles

Explanation:

We are given the total distance = 400 miles and total time taken = 7 hours

Given the average rate till interstate route is reached = 50 miles per hour and then rate is increased to 60 miles per hour till end of the trip.  

Let x be the distance from starting till interstate route

so time taken is given by  [tex]\frac{x}{50}[/tex]

and time taken for rest of the journey = [tex]\frac{(400-\mathrm{x})}{60}[/tex]  as total distance = 400

Since, total time for journey = 7 hours ,  

we get equation

  [tex]\left(\frac{x}{50}+\frac{(400-x)}{60}\right)=7[/tex]

=> 60x + 20000 - 50x = 21000

which gives x = 100 which is the required answer  

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