Question

Greg drove at a constant speed in a rainstorm for 245 245 miles. he took a​ break, and the rain stopped he then drove 160 160 miles at a speed that was 5 5 miles per hour faster than his previous speed. if he drove for 11 11 ​hours, find the​ car's speed for each part of the trip.

Answer 1

distance = rate x time

245 = r * t

160 = (r+5)(11-t)

260 = 11r - rt + 55 - 5t

= 11r - 245 + 55 - 5t

160= 11r - 190 – 5t

350 = 11r - 5t

rt = 245 ---> t = 245/r

350 = 11r - 5(245/r)

350 = 11r - 1225/r

350r = 11r^2 - 1225

0 = 11r^2 - 350r - 1225

0 = (11r + 35)(r-35)

11r + 35 = 0 results in negative rates and times

r-35 = 0 --> r = 35.

He drove 35 mph for 245/35 = 7 hours in the rain.

He then drove 42 mph for 6 hours. That's 42 * 6 = 252 miles.