Greg drove at a constant speed in a rainstorm for 246 miles. He took a​ break, and the rain stopped He then drove 235 miles at a speed that was 6

Question

 Greg drove at a constant speed in a rainstorm for
246
 miles. He took a break, and the rain stopped He then drove

235 miles at a speed that was

6 miles per hour faster than his previous speed. If he drove for

11 hours, find the car's speed for each part of the trip.

Answer 1

 

 

distance = rate x time

 

246 = r * t

 

235 =  (r+6)(11-t)

 

235 = 11r - rt + 66 - 6t

 

       = 11r - 246 + 66 - 6t

 

235 = 11r - 180 - 6t

 

415 = 11r - 6t

 

rt  = 246 ---> t = 246/r

 

415 = 11r - 6(246/r)

 

415 = 11r - 1476/r

 

415r = 11r^2 - 1476

 

0 = 11r^2 - 415r - 1476

 

0 = ( 11r     + 36    )(r   - 41            )

 

11r + 36 = 0   results in negative rates and times

 

r-41 = 0 --> r = 41.

 

He drove 41 mph for 246/41 = 6 hours in the rain.

 

He then drove 47 mph for 5 hours. That's 47 * 5 = 235 miles.