Word Problem

Question

Johnny was able to drive an average of 15 miles per hour faster in his car after the traffic cleared. He drove 38 miles in traffic before it cleared and then drove another 170 miles. If the total trip took 7 hours, then what was his average speed in traffic?

Answer 1

 

  38 = R * T

 

  170 = (R+15)*(7-T)

 

         = 7R - RT + 105 - 15T

 

 

         = 7R - 38 + 105 - 15T

 

          = 7R  +67 - 15T

 

So 103 = 7R - 15T ---> (15T + 103)/7 = R

    RT = 38

 

 

  (15T +103)/7 * T = 38

 

(15T + 103)T = 266

 

 15T^2 + 103T - 266 = 0

 

 

(15T + 133)(T-2) = 0

 

 

15T + 133 = 0  results in negative times

 

T-2= 0 ---> T = 2

 

So stuck in traffic, he travels

19 mph for 2 hours, which is 38 miles

He then travels 19+15 = 34 mph for 5 hours = 170 miles

 

Stuck in traffic: 19 mph

In the clear: 34 mph

average speed (38+170)/7 = 29 and 5/7 mph