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

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