Question

Johnny was able to drive an average of 31 miles per hour faster in his car after the traffic cleared. He drove 16 miles in traffic before it cleared and then drove another 47 miles. If the total trip took 2 hours, then what was his average speed in traffic?

Answer 1

9514 1404 393

Answer:

16 mi/h

Explanation:

The time for a given leg of the trip is the distance divided by the speed. If t is the speed in traffic, the total trip time is ...

16/t +47/(t+31) = 2

Multiplying by t(t+31), we get ...

16(t +31) +47t = 2(t)(t+31)

2t^2 -t -496 = 0 . . . . put in standard form

(2t +31)(t -16) = 0 . . . . factor

The positive solution is t = 16.

Johhny's average speed in traffic was 16 mph.