Greg drove at a constant speed

Question

Greg drove at a constant speed in a rainstorm for 280 miles. He took a break, and the rain stopped He then drove 220 miles at a speed that was 9 miles per hour faster than his previous speed. If he drove for 13 hours, find the car's speed for each part of the trip.

Answer 1

Distance = Rate x Time

 

280 = R x (13-T) <--- driving while raining

 

220 = (R+9)*T  <-- 9 mph faster , no rain

 

 

Solves each equation for T:

 

1st equation:

 

280/R = 13 - T

 

280/R - 13 = -T

 

13 - 280/R = T

 

 

2nd equation:

220 = (R+9)*T

T = 220/(R+9)

 

13 - 280/R = 220/(R+9)

 

13R - 280           220

----------  =  -------------

    R                R + 9

 

Cross Multiplies:

 

(13R - 280)(R + 9) = 220R

 

(13R - 280)(R + 9) - 220R = 0

 

13R^2 + 117R - 280R - 2520 - 220R = 0

 

13R^2 - 383R - 2520 = 0

 

(13R   +   72)(R     -     35 ) = 0

 

13R + 72 = 0 OR R - 35 = 0

 

R = -72/13  OR R = 35

 

Since the rate of speed cannot be negative,

the first solution is disqualified and rejected.

 

So R is 35.

 

Greg drove 280 miles at 35 mph, in t = 280/35 = 8 hours

 

Greg drove 220 miles at 44 mph, in t = 220/44 = 5 hours